better explanations of vector outputs for compute temp commands

doc/src/compute_temp.rst

@@ -48,13 +48,17 @@ the group, :math:`N_\mathrm{fix DOFs}` is the number of degrees of
 freedom removed by fix commands (see below), :math:`k_B` is the
 Boltzmann constant, and :math:`T` is the resulting computed temperature.
 
-A kinetic energy tensor, stored as a six-element vector, is also
+A symmetric tensor, stored as a six-element vector, is also calculated
-calculated by this compute for use in the computation of a pressure
+by this compute for use in the computation of a pressure tensor by the
-tensor.  The formula for the components of the tensor is the same as the
+:doc:`compute pressue <compute_pressure>` command.  The formula for
-above expression for :math:`E_\mathrm{kin}`, except that :math:`v_i^2` is
+the components of the tensor is the same as the above expression for
-replaced by :math:`v_{i,x} v_{i,y}` for the :math:`xy` component, and so on.
+:math:`E_\mathrm{kin}`, except that the 1/2 factor is NOT included and
-The six components of the vector are ordered :math:`xx`, :math:`yy`,
+the :math:`v_i^2` is replaced by :math:`v_{i,x} v_{i,y}` for the
-:math:`zz`, :math:`xy`, :math:`xz`, :math:`yz`.
+:math:`xy` component, and so on.  Note that because it lacks the 1/2
+factor, these tensor components are twice those of the traditional
+kinetic energy tensor.  The six components of the vector are ordered
+:math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`,
+:math:`yz`.
       
 The number of atoms contributing to the temperature is assumed to be
 constant for the duration of the run; use the *dynamic* option of the
@@ -94,16 +98,17 @@ Output info
 """""""""""
 
 This compute calculates a global scalar (the temperature) and a global
-vector of length six (KE tensor), which can be accessed by indices
+vector of length six (symmetric tensor), which can be accessed by
-1--6.  These values can be used by any command that uses global scalar
+indices 1--6.  These values can be used by any command that uses
-or vector values from a compute as input.  See the :doc:`Howto output
+global scalar or vector values from a compute as input.  See the
-<Howto_output>` page for an overview of LAMMPS output options.
+:doc:`Howto output <Howto_output>` page for an overview of LAMMPS
+output options.
 
 The scalar value calculated by this compute is "intensive".  The
 vector values are "extensive".
 
-The scalar value will be in temperature :doc:`units <units>`.  The
+The scalar value is in temperature :doc:`units <units>`.  The vector
-vector values will be in energy :doc:`units <units>`.
+values are in energy :doc:`units <units>`.
 
 Restrictions
 """"""""""""

doc/src/compute_temp_asphere.rst

@@ -90,6 +90,19 @@ for the :math:`xy` component, and the appropriate elements of the moment of
 inertia tensor are used.  The six components of the vector are ordered
 :math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`, :math:`yz`.
 
+A symmetric tensor, stored as a six-element vector, is also calculated
+by this compute for use in the computation of a pressure tensor by the
+:doc:`compute pressue <compute_pressure>` command.  The formula for
+the components of the tensor is the same as the above expression for
+:math:`E_\mathrm{kin}`, except that the 1/2 factor is NOT included and
+the :math:`v_i^2` and :math:`\omega^2` are replaced by :math:`v_x v_y`
+and :math:`\omega_x \omega_y` for the :math:`xy` component, and so on.
+And the appropriate elements of the moment of inertia tensor are used.
+Note that because it lacks the 1/2 factor, these tensor components are
+twice those of the traditional kinetic energy tensor.  The six
+components of the vector are ordered :math:`xx`, :math:`yy`,
+:math:`zz`, :math:`xy`, :math:`xz`, :math:`yz`.
+
 The number of atoms contributing to the temperature is assumed to be
 constant for the duration of the run; use the *dynamic/dof* option of
 the :doc:`compute_modify <compute_modify>` command if this is not the
@@ -131,17 +144,17 @@ Output info
 """""""""""
 
 This compute calculates a global scalar (the temperature) and a global
-vector of length 6 (KE tensor), which can be accessed by indices 1--6.
+vector of length 6 (symmertic tensor), which can be accessed by
-These values can be used by any command that uses global scalar or
+indices 1--6.  These values can be used by any command that uses
-vector values from a compute as input.
+global scalar or vector values from a compute as input.  See the
-See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS
+:doc:`Howto output <Howto_output>` page for an overview of LAMMPS
 output options.
 
 The scalar value calculated by this compute is "intensive".  The
 vector values are "extensive".
 
-The scalar value will be in temperature :doc:`units <units>`.  The
+The scalar value is in temperature :doc:`units <units>`.  The vector
-vector values will be in energy :doc:`units <units>`.
+values are in energy :doc:`units <units>`.
 
 Restrictions
 """"""""""""

doc/src/compute_temp_body.rst

@@ -62,12 +62,17 @@ kinetic energy is computed as :math:`\frac12 I \omega^2`, where :math:`I`
 is the moment of inertia tensor for the aspherical particle and :math:`\omega`
 is its angular velocity, which is computed from its angular momentum.
 
-A kinetic energy tensor, stored as a 6-element vector, is also calculated by
+A symmetric tensor, stored as a six-element vector, is also calculated
-this compute.  The formula for the components of the tensor is the same as the
+by this compute for use in the computation of a pressure tensor by the
-above formula, except that :math:`v^2` and :math:`\omega^2` are
+:doc:`compute pressue <compute_pressure>` command.  The formula for
-replaced by :math:`v_x v_y` and :math:`\omega_x \omega_y` for the
+the components of the tensor is the same as the above expression for
-math:`xy` component, and the appropriate elements of the inertia tensor are
+:math:`E_\mathrm{kin}`, except that the 1/2 factor is NOT included and
-used.  The six components of the vector are ordered :math:`xx`, :math:`yy`,
+the :math:`v_i^2` and :math:`\omega^2` are replaced by :math:`v_x v_y`
+and :math:`\omega_x \omega_y` for the :math:`xy` component, and so on.
+And the appropriate elements of the moment of inertia tensor are used.
+Note that because it lacks the 1/2 factor, these tensor components are
+twice those of the traditional kinetic energy tensor.  The six
+components of the vector are ordered :math:`xx`, :math:`yy`,
 :math:`zz`, :math:`xy`, :math:`xz`, :math:`yz`.
 
 The number of atoms contributing to the temperature is assumed to be
@@ -111,17 +116,17 @@ Output info
 """""""""""
 
 This compute calculates a global scalar (the temperature) and a global
-vector of length 6 (KE tensor), which can be accessed by indices 1--6.
+vector of length 6 (symmetric tensor), which can be accessed by
-These values can be used by any command that uses global scalar or
+indices 1--6.  These values can be used by any command that uses
-vector values from a compute as input.
+global scalar or vector values from a compute as input.  See the
-See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS
+:doc:`Howto output <Howto_output>` page for an overview of LAMMPS
 output options.
 
 The scalar value calculated by this compute is "intensive".  The
 vector values are "extensive".
 
-The scalar value will be in temperature :doc:`units <units>`.
+The scalar value is in temperature :doc:`units <units>`.  The vector
-The vector values will be in energy :doc:`units <units>`.
+values are in energy :doc:`units <units>`.
 
 Restrictions
 """"""""""""

doc/src/compute_temp_chunk.rst

@@ -85,12 +85,14 @@ By default, *adof* = 2 or 3 = dimensionality of system, as set via the
 :doc:`dimension <dimension>` command, and *cdof* = 0.0.
 This gives the usual formula for temperature.
 
-A kinetic energy tensor, stored as a six-element vector, is also
+A symmetric tensor, stored as a six-element vector, is also calculated
-calculated by this compute for use in the computation of a pressure
+by this compute.  The formula for the components of the tensor is the
-tensor.  The formula for the components of the tensor is the same as
+same as the above expression for :math:`E_\mathrm{kin}`, except that
-the above formula, except that :math:`v^2` is replaced by
+the 1/2 factor is NOT included and the :math:`v_i^2` is replaced by
-:math:`v_x v_y` for the :math:`xy` component, and so on.
+:math:`v_{i,x} v_{i,y}` for the :math:`xy` component, and so on.  Note
-The six components of the vector are ordered :math:`xx`, :math:`yy`,
+that because it lacks the 1/2 factor, these tensor components are
+twice those of the traditional kinetic energy tensor.  The six
+components of the vector are ordered :math:`xx`, :math:`yy`,
 :math:`zz`, :math:`xy`, :math:`xz`, :math:`yz`.
 
 Note that the number of atoms contributing to the temperature is
@@ -227,10 +229,10 @@ Output info
 """""""""""
 
 This compute calculates a global scalar (the temperature) and a global
-vector of length 6 (KE tensor), which can be accessed by indices 1--6.
+vector of length 6 (symmetric tensor), which can be accessed by
-These values can be used by any command that uses global scalar or
+indices 1--6.  These values can be used by any command that uses
-vector values from a compute as input.
+global scalar or vector values from a compute as input.  See the
-See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS
+:doc:`Howto output <Howto_output>` page for an overview of LAMMPS
 output options.
 
 This compute also optionally calculates a global array, if one or more
@@ -245,9 +247,9 @@ page for an overview of LAMMPS output options.
 The scalar value calculated by this compute is "intensive".  The
 vector values are "extensive".  The array values are "intensive".
 
-The scalar value will be in temperature :doc:`units <units>`.  The
+The scalar value is in temperature :doc:`units <units>`.  The vector
-vector values will be in energy :doc:`units <units>`.  The array values
+values are in energy :doc:`units <units>`.  The array values will be
-will be in temperature :doc:`units <units>` for the *temp* value, and in
+in temperature :doc:`units <units>` for the *temp* value, and in
 energy :doc:`units <units>` for the *kecom* and *internal* values.
 
 Restrictions

doc/src/compute_temp_com.rst

@@ -44,12 +44,17 @@ where KE is the total kinetic energy of the group of atoms (sum of
 simulation, :math:`N` is number of atoms in the group, :math:`k_B` is
 the Boltzmann constant, and :math:`T` is the absolute temperature.
 
-A kinetic energy tensor, stored as a six-element vector, is also
+A symmetric tensor, stored as a six-element vector, is also calculated
-calculated by this compute for use in the computation of a pressure
+by this compute for use in the computation of a pressure tensor by the
-tensor.  The formula for the components of the tensor is the same as
+:doc:`compute pressue <compute_pressure>` command.  The formula for
-the above formula, except that :math:`v^2` is replaced by :math:`v_x v_y`
+the components of the tensor is the same as the above expression for
-for the :math:`xy` component, and so on.  The six components of the vector are
+:math:`E_\mathrm{kin}`, except that the 1/2 factor is NOT included and
-ordered :math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`, :math:`yz`.
+the :math:`v_i^2` is replaced by :math:`v_{i,x} v_{i,y}` for the
+:math:`xy` component, and so on.  Note that because it lacks the 1/2
+factor, these tensor components are twice those of the traditional
+kinetic energy tensor.  The six components of the vector are ordered
+:math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`,
+:math:`yz`.
 
 The number of atoms contributing to the temperature is assumed to be
 constant for the duration of the run; use the *dynamic* option of the
@@ -81,17 +86,17 @@ Output info
 """""""""""
 
 This compute calculates a global scalar (the temperature) and a global
-vector of length 6 (KE tensor), which can be accessed by indices 1--6.
+vector of length 6 (symmetric tensor), which can be accessed by
-These values can be used by any command that uses global scalar or
+indices 1--6.  These values can be used by any command that uses
-vector values from a compute as input.  See the
+global scalar or vector values from a compute as input.  See the
-:doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
+:doc:`Howto output <Howto_output>` page for an overview of LAMMPS
-options.
+output options.
 
 The scalar value calculated by this compute is "intensive".  The
 vector values are "extensive".
 
-The scalar value will be in temperature :doc:`units <units>`.
+The scalar value is in temperature :doc:`units <units>`.  The vector
-The vector values will be in energy :doc:`units <units>`.
+values is in energy :doc:`units <units>`.
 
 Restrictions
 """"""""""""

doc/src/compute_temp_cs.rst

@@ -67,26 +67,31 @@ the velocity of each core or shell atom used in the KE calculation is
 the velocity of the center-of-mass (COM) of the core/shell pair the
 atom is part of.
 
-A kinetic energy tensor, stored as a six-element vector, is also calculated by
+A symmetric tensor, stored as a six-element vector, is also calculated
-this compute for use in the computation of a pressure tensor.  The formula for
+by this compute for use in the computation of a pressure tensor by the
-the components of the tensor is the same as the above formula, except that
+:doc:`compute pressue <compute_pressure>` command.  The formula for
-:math:`v^2` is replaced by :math:`v_x v_y` for the :math:`xy` component, and so
+the components of the tensor is the same as the above expression for
-on. The six components of the vector are ordered :math:`xx`, :math:`yy`,
+:math:`E_\mathrm{kin}`, except that the 1/2 factor is NOT included and
-:math:`zz`, :math:`xy`, :math:`xz`, :math:`yz`. In contrast to the temperature,
+the :math:`v_i^2` is replaced by :math:`v_{i,x} v_{i,y}` for the
-the velocity of each core or shell atom is taken individually.
+:math:`xy` component, and so on.  Note that because it lacks the 1/2
+factor, these tensor components are twice those of the traditional
+kinetic energy tensor.  The six components of the vector are ordered
+:math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`,
+:math:`yz`.
 
 The change this fix makes to core/shell atom velocities is essentially
-computing the temperature after a "bias" has been removed from the velocity of
+computing the temperature after a "bias" has been removed from the
-the atoms.  This "bias" is the velocity of the atom relative to the
+velocity of the atoms.  This "bias" is the velocity of the atom
-center-of-mass velocity of the core/shell pair.  If this compute is used with a
+relative to the center-of-mass velocity of the core/shell pair.  If
-fix command that performs thermostatting then this bias will be subtracted from
+this compute is used with a fix command that performs thermostatting
-each atom, thermostatting of the remaining center-of-mass velocity will be
+then this bias will be subtracted from each atom, thermostatting of
-performed, and the bias will be added back in.  This means the thermostatting
+the remaining center-of-mass velocity will be performed, and the bias
-will effectively be performed on the core/shell pairs, instead of on the
+will be added back in.  This means the thermostatting will effectively
-individual core and shell atoms.  Thermostatting fixes that work in this way
+be performed on the core/shell pairs, instead of on the individual
-include :doc:`fix nvt <fix_nh>`, :doc:`fix temp/rescale <fix_temp_rescale>`,
+core and shell atoms.  Thermostatting fixes that work in this way
-:doc:`fix temp/berendsen <fix_temp_berendsen>`, and
+include :doc:`fix nvt <fix_nh>`, :doc:`fix temp/rescale
-:doc:`fix langevin <fix_langevin>`.
+<fix_temp_rescale>`, :doc:`fix temp/berendsen <fix_temp_berendsen>`,
+and :doc:`fix langevin <fix_langevin>`.
 
 The internal energy of core/shell pairs can be calculated by the
 :doc:`compute temp/chunk <compute_temp_chunk>` command, if chunks are defined
@@ -97,15 +102,15 @@ Output info
 """""""""""
 
 This compute calculates a global scalar (the temperature) and a global
-vector of length 6 (KE tensor), which can be accessed by indices 1--6.
+vector of length 6 (symmertric tensor), which can be accessed by
-These values can be used by any command that uses global scalar or
+indices 1--6.  These values can be used by any command that uses
-vector values from a compute as input.
+global scalar or vector values from a compute as input.
 
 The scalar value calculated by this compute is "intensive".  The
 vector values are "extensive".
 
-The scalar value will be in temperature :doc:`units <units>`.  The
+The scalar value is in temperature :doc:`units <units>`.  The vector
-vector values will be in energy :doc:`units <units>`.
+values are in energy :doc:`units <units>`.
 
 Restrictions
 """"""""""""

doc/src/compute_temp_deform.rst

@@ -73,12 +73,16 @@ simulation, :math:`N` is the number of atoms in the group, :math:`k_B`
 is the Boltzmann constant, and :math:`T` is the temperature.  Note that
 :math:`v` in the kinetic energy formula is the atom's velocity.
 
-A kinetic energy tensor, stored as a six-element vector, is also
+A symmetric tensor, stored as a six-element vector, is also calculated
-calculated by this compute for use in the computation of a pressure
+by this compute for use in the computation of a pressure tensor by the
-tensor.  The formula for the components of the tensor is the same as
+:doc:`compute pressue <compute_pressure>` command.  The formula for
-the above formula, except that :math:`v^2` is replaced by :math:`v_x v_y` for
+the components of the tensor is the same as the above expression for
-the :math:`xy` component, and so on. The six components of the vector are
+:math:`E_\mathrm{kin}`, except that the 1/2 factor is NOT included and
-ordered :math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`,
+the :math:`v_i^2` is replaced by :math:`v_{i,x} v_{i,y}` for the
+:math:`xy` component, and so on.  Note that because it lacks the 1/2
+factor, these tensor components are twice those of the traditional
+kinetic energy tensor.  The six components of the vector are ordered
+:math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`,
 :math:`yz`.
 
 The number of atoms contributing to the temperature is assumed to be
@@ -128,17 +132,17 @@ Output info
 """""""""""
 
 This compute calculates a global scalar (the temperature) and a global
-vector of length 6 (KE tensor), which can be accessed by indices 1--6.
+vector of length 6 (symmetric tensor), which can be accessed by
-These values can be used by any command that uses global scalar or
+indices 1--6.  These values can be used by any command that uses
-vector values from a compute as input.  See the
+global scalar or vector values from a compute as input.  See the
-:doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
+:doc:`Howto output <Howto_output>` page for an overview of LAMMPS
-options.
+output options.
 
 The scalar value calculated by this compute is "intensive".  The
 vector values are "extensive".
 
-The scalar value will be in temperature :doc:`units <units>`.
+The scalar value is in temperature :doc:`units <units>`.  The vector
-The vector values will be in energy :doc:`units <units>`.
+values are in energy :doc:`units <units>`.
 
 Restrictions
 """"""""""""

doc/src/compute_temp_deform_eff.rst

@@ -29,17 +29,20 @@ model, after subtracting out a streaming velocity induced by the
 simulation box changing size and/or shape, for example in a
 non-equilibrium MD (NEMD) simulation.  The size/shape change is
 induced by use of the :doc:`fix deform <fix_deform>` command.  A
-compute of this style is created by the
+compute of this style is created by the :doc:`fix nvt/sllod/eff
-:doc:`fix nvt/sllod/eff <fix_nvt_sllod_eff>` command to compute the thermal
+<fix_nvt_sllod_eff>` command to compute the thermal temperature of
-temperature of atoms for thermostatting purposes.  A compute of this
+atoms for thermostatting purposes.  A compute of this style can also
-style can also be used by any command that computes a temperature
+be used by any command that computes a temperature (e.g.,
-(e.g., :doc:`thermo_modify <thermo_modify>`, :doc:`fix npt/eff <fix_nh_eff>`).
+:doc:`thermo_modify <thermo_modify>`, :doc:`fix npt/eff
+<fix_nh_eff>`).
 
 The calculation performed by this compute is exactly like that
 described by the :doc:`compute temp/deform <compute_temp_deform>`
-command, except that the formula for the temperature includes the
+command, except that the formulas for the temperature (scalar) and
-radial electron velocity contributions, as discussed by the :doc:`compute temp/eff <compute_temp_eff>` command.  Note that only the
+diagonal components of the symmetric tensor (vector) include the
-translational degrees of freedom for each nuclei or electron are
+radial electron velocity contributions, as discussed by the
+:doc:`compute temp/eff <compute_temp_eff>` command.  Note that only
+the translational degrees of freedom for each nuclei or electron are
 affected by the streaming velocity adjustment.  The radial velocity
 component of the electrons is not affected.
 
@@ -47,17 +50,17 @@ Output info
 """""""""""
 
 This compute calculates a global scalar (the temperature) and a global
-vector of length 6 (KE tensor), which can be accessed by indices 1--6.
+vector of length 6 (symmetric tensor), which can be accessed by
-These values can be used by any command that uses global scalar or
+indices 1--6.  These values can be used by any command that uses
-vector values from a compute as input.  See the
+global scalar or vector values from a compute as input.  See the
-:doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
+:doc:`Howto output <Howto_output>` page for an overview of LAMMPS
-options.
+output options.
 
 The scalar value calculated by this compute is "intensive".  The
 vector values are "extensive".
 
-The scalar value will be in temperature :doc:`units <units>`.  The
+The scalar value is in temperature :doc:`units <units>`.  The vector
-vector values will be in energy :doc:`units <units>`.
+values are in energy :doc:`units <units>`.
 
 Restrictions
 """"""""""""

doc/src/compute_temp_partial.rst

@@ -44,12 +44,16 @@ constant, and :math:`T` = temperature.  The calculation of KE excludes the
 is 0.  The dim parameter is adjusted to give the correct number of
 degrees of freedom.
 
-A kinetic energy tensor, stored as a six-element vector, is also
+A symmetric tensor, stored as a six-element vector, is also calculated
-calculated by this compute for use in the calculation of a pressure
+by this compute for use in the computation of a pressure tensor by the
-tensor.  The formula for the components of the tensor is the same as
+:doc:`compute pressue <compute_pressure>` command.  The formula for
-the above formula, except that :math:`v^2` is replaced by :math:`v_x v_y` for
+the components of the tensor is the same as the above expression for
-the :math:`xy` component, and so on. The six components of the vector are
+:math:`E_\mathrm{kin}`, except that the 1/2 factor is NOT included and
-ordered :math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`,
+the :math:`v_i^2` is replaced by :math:`v_{i,x} v_{i,y}` for the
+:math:`xy` component, and so on.  Note that because it lacks the 1/2
+factor, these tensor components are twice those of the traditional
+kinetic energy tensor.  The six components of the vector are ordered
+:math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`,
 :math:`yz`.
 
 The number of atoms contributing to the temperature is assumed to be
@@ -88,17 +92,17 @@ Output info
 """""""""""
 
 This compute calculates a global scalar (the temperature) and a global
-vector of length 6 (KE tensor), which can be accessed by indices 1--6.
+vector of length 6 (symmetric tensor), which can be accessed by
-These values can be used by any command that uses global scalar or
+indices 1--6.  These values can be used by any command that uses
-vector values from a compute as input.
+global scalar or vector values from a compute as input.  See the
-See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS
+:doc:`Howto output <Howto_output>` page for an overview of LAMMPS
 output options.
 
 The scalar value calculated by this compute is "intensive".  The
 vector values are "extensive".
 
-The scalar value will be in temperature :doc:`units <units>`.  The
+The scalar value is in temperature :doc:`units <units>`.  The vector
-vector values will be in energy :doc:`units <units>`.
+values are in energy :doc:`units <units>`.
 
 Restrictions
 """"""""""""

doc/src/compute_temp_profile.rst

@@ -97,21 +97,27 @@ center-of-mass velocity across the group in directions where streaming velocity
 is *not* subtracted. This can be altered using the *extra* option of the
 :doc:`compute_modify <compute_modify>` command.
 
-If the *out* keyword is used with a *tensor* value, which is the default,
+If the *out* keyword is used with a *tensor* value, which is the
-a kinetic energy tensor, stored as a six-element vector, is also calculated by
+default, then a symmetric tensor, stored as a six-element vector, is
-this compute for use in the computation of a pressure tensor.  The formula for
+also calculated by this compute for use in the computation of a
-the components of the tensor is the same as the above formula, except that
+pressure tensor by the :doc:`compute pressue <compute_pressure>`
-:math:`v^2` is replaced by :math:`v_x v_y` for the :math:`xy` component, and
+command.  The formula for the components of the tensor is the same as
-so on.  The six components of the vector are ordered :math:`xx`, :math:`yy`,
+the above expression for :math:`E_\mathrm{kin}`, except that the 1/2
+factor is NOT included and the :math:`v_i^2` is replaced by
+:math:`v_{i,x} v_{i,y}` for the :math:`xy` component, and so on.  Note
+that because it lacks the 1/2 factor, these tensor components are
+twice those of the traditional kinetic energy tensor.  The six
+components of the vector are ordered :math:`xx`, :math:`yy`,
 :math:`zz`, :math:`xy`, :math:`xz`, :math:`yz`.
 
-If the *out* keyword is used with a *bin* value, the count of atoms and
+If the *out* keyword is used with a *bin* value, the count of atoms
-computed temperature for each bin are stored for output, as an array of values,
+and computed temperature for each bin are stored for output, as an
-as described below.  The temperature of each bin is calculated as described
+array of values, as described below.  The temperature of each bin is
-above, where the bias velocity is subtracted and only the remaining thermal
+calculated as described above, where the bias velocity is subtracted
-velocity of atoms in the bin contributes to the temperature.  See the note
+and only the remaining thermal velocity of atoms in the bin
-below for how the temperature is normalized by the degrees-of-freedom of atoms
+contributes to the temperature.  See the note below for how the
-in the bin.
+temperature is normalized by the degrees-of-freedom of atoms in the
+bin.
 
 The number of atoms contributing to the temperature is assumed to be
 constant for the duration of the run; use the *dynamic* option of the
@@ -166,16 +172,17 @@ Output info
 This compute calculates a global scalar (the temperature).  Depending
 on the setting of the *out* keyword, it also calculates a global
 vector or array.  For *out* = *tensor*, it calculates a vector of
-length 6 (KE tensor), which can be accessed by indices 1--6.  For *out*
+length 6 (symmetric tensor), which can be accessed by indices 1--6.
-= *bin* it calculates a global array which has 2 columns and :math:`N` rows,
+For *out* = *bin* it calculates a global array which has 2 columns and
-where :math:`N` is the number of bins.  The first column contains the number
+:math:`N` rows, where :math:`N` is the number of bins.  The first
-of atoms in that bin.  The second contains the temperature of that
+column contains the number of atoms in that bin.  The second contains
-bin, calculated as described above.  The ordering of rows in the array
+the temperature of that bin, calculated as described above.  The
-is as follows.  Bins in :math:`x` vary fastest, then :math:`y`, then
+ordering of rows in the array is as follows.  Bins in :math:`x` vary
-:math:`z`.  Thus for a :math:`10\times 10\times 10` 3d array of bins, there
+fastest, then :math:`y`, then :math:`z`.  Thus for a :math:`10\times
-will be 1000 rows.  The bin with indices :math:`(i_x,i_y,i_z) = (2,3,4)` would
+10\times 10` 3d array of bins, there will be 1000 rows.  The bin with
-map to row :math:`M = 10^2(i_z-1)  + 10(i_y-1) + i_x = 322`, where the rows are
+indices :math:`(i_x,i_y,i_z) = (2,3,4)` would map to row :math:`M =
-numbered from 1 to 1000 and the bin indices are numbered from 1 to 10 in each
+10^2(i_z-1) + 10(i_y-1) + i_x = 322`, where the rows are numbered from
+1 to 1000 and the bin indices are numbered from 1 to 10 in each
 dimension.
 
 These values can be used by any command that uses global scalar or
@@ -186,9 +193,9 @@ options.
 The scalar value calculated by this compute is "intensive".  The
 vector values are "extensive".  The array values are "intensive".
 
-The scalar value will be in temperature :doc:`units <units>`.  The
+The scalar value us in temperature :doc:`units <units>`.  The vector
-vector values will be in energy :doc:`units <units>`.  The first column
+values are in energy :doc:`units <units>`.  The first column of array
-of array values are counts; the values in the second column will be in
+values are counts; the values in the second column will be in
 temperature :doc:`units <units>`.
 
 Restrictions
@@ -203,7 +210,10 @@ will be for most thermostats.
 Related commands
 """"""""""""""""
 
-:doc:`compute temp <compute_temp>`, :doc:`compute temp/ramp <compute_temp_ramp>`, :doc:`compute temp/deform <compute_temp_deform>`, :doc:`compute pressure <compute_pressure>`
+:doc:`compute temp <compute_temp>`, :doc:`compute temp/ramp
+     <compute_temp_ramp>`, :doc:`compute temp/deform
+     <compute_temp_deform>`, :doc:`compute pressure
+     <compute_pressure>`
 
 Default
 """""""

doc/src/compute_temp_ramp.rst

@@ -63,12 +63,17 @@ command (e.g., :math:`\AA` for units = real or metal).  A
 velocity in lattice spacings per unit time).  The :doc:`lattice <lattice>`
 command must have been previously used to define the lattice spacing.
 
-A kinetic energy tensor, stored as a six-element vector, is also calculated by
+A symmetric tensor, stored as a six-element vector, is also calculated
-this compute for use in the computation of a pressure tensor.  The formula for
+by this compute for use in the computation of a pressure tensor by the
-the components of the tensor is the same as the above formula, except that
+:doc:`compute pressue <compute_pressure>` command.  The formula for
-:math:`v^2` is replaced by :math:`v_x v_y` for the :math:`xy` component, and
+the components of the tensor is the same as the above expression for
-so on.  The six components of the vector are ordered :math:`xx`, :math:`yy`,
+:math:`E_\mathrm{kin}`, except that the 1/2 factor is NOT included and
-:math:`zz`, :math:`xy`, :math:`xz`, :math:`yz`.
+the :math:`v_i^2` is replaced by :math:`v_{i,x} v_{i,y}` for the
+:math:`xy` component, and so on.  Note that because it lacks the 1/2
+factor, these tensor components are twice those of the traditional
+kinetic energy tensor.  The six components of the vector are ordered
+:math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`,
+:math:`yz`.
 
 The number of atoms contributing to the temperature is assumed to be constant
 for the duration of the run; use the *dynamic* option of the
@@ -100,17 +105,17 @@ Output info
 """""""""""
 
 This compute calculates a global scalar (the temperature) and a global
-vector of length 6 (KE tensor), which can be accessed by indices 1--6.
+vector of length 6 (symmetric tensor), which can be accessed by
-These values can be used by any command that uses global scalar or
+indices 1--6.  These values can be used by any command that uses
-vector values from a compute as input.  See the
+global scalar or vector values from a compute as input.  See the
-:doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
+:doc:`Howto output <Howto_output>` page for an overview of LAMMPS
-options.
+output options.
 
 The scalar value calculated by this compute is "intensive".  The
 vector values are "extensive".
 
-The scalar value will be in temperature :doc:`units <units>`.  The
+The scalar value is in temperature :doc:`units <units>`.  The vector
-vector values will be in energy :doc:`units <units>`.
+values are in energy :doc:`units <units>`.
 
 Restrictions
 """"""""""""
@@ -119,7 +124,10 @@ Restrictions
 Related commands
 """"""""""""""""
 
-:doc:`compute temp <compute_temp>`, :doc:`compute temp/profie <compute_temp_profile>`, :doc:`compute temp/deform <compute_temp_deform>`, :doc:`compute pressure <compute_pressure>`
+:doc:`compute temp <compute_temp>`, :doc:`compute temp/profie
+     <compute_temp_profile>`, :doc:`compute temp/deform
+     <compute_temp_deform>`, :doc:`compute pressure
+     <compute_pressure>`
 
 Default
 """""""

doc/src/compute_temp_region.rst

@@ -49,12 +49,17 @@ where KE = is the total kinetic energy of the group of atoms (sum of
 :math:`N` is the  number of atoms in both the group and region, :math:`k_B` is
 the Boltzmann constant, and :math:`T` temperature.
 
-A kinetic energy tensor, stored as a six-element vector, is also
+A symmetric tensor, stored as a six-element vector, is also calculated
-calculated by this compute for use in the computation of a pressure
+by this compute for use in the computation of a pressure tensor by the
-tensor.  The formula for the components of the tensor is the same as
+:doc:`compute pressue <compute_pressure>` command.  The formula for
-the above formula, except that :math:`v^2` is replaced by :math:`v_x v_y`
+the components of the tensor is the same as the above expression for
-for the :math:`xy` component, and so on.  The six components of the vector are
+:math:`E_\mathrm{kin}`, except that the 1/2 factor is NOT included and
-ordered :math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`, :math:`yz`.
+the :math:`v_i^2` is replaced by :math:`v_{i,x} v_{i,y}` for the
+:math:`xy` component, and so on.  Note that because it lacks the 1/2
+factor, these tensor components are twice those of the traditional
+kinetic energy tensor.  The six components of the vector are ordered
+:math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`,
+:math:`yz`.
 
 The number of atoms contributing to the temperature is calculated each
 time the temperature is evaluated since it is assumed atoms can
@@ -78,12 +83,13 @@ will operate only on atoms that are currently in the geometric region.
 
 Unlike other compute styles that calculate temperature, this compute
 does not subtract out degrees-of-freedom due to fixes that constrain
-motion, such as :doc:`fix shake <fix_shake>` and :doc:`fix rigid <fix_rigid>`.  This is because those degrees of freedom
+motion, such as :doc:`fix shake <fix_shake>` and :doc:`fix rigid
-(e.g., a constrained bond) could apply to sets of atoms that straddle
+<fix_rigid>`.  This is because those degrees of freedom (e.g., a
-the region boundary, and hence the concept is somewhat ill-defined.
+constrained bond) could apply to sets of atoms that straddle the
-If needed the number of subtracted degrees of freedom can be set
+region boundary, and hence the concept is somewhat ill-defined.  If
-explicitly using the *extra* option of the
+needed the number of subtracted degrees of freedom can be set
-:doc:`compute_modify <compute_modify>` command.
+explicitly using the *extra* option of the :doc:`compute_modify
+<compute_modify>` command.
 
 See the :doc:`Howto thermostat <Howto_thermostat>` page for a
 discussion of different ways to compute temperature and perform
@@ -93,17 +99,17 @@ Output info
 """""""""""
 
 This compute calculates a global scalar (the temperature) and a global
-vector of length 6 (KE tensor), which can be accessed by indices 1--6.
+vector of length 6 (symmetric tensor), which can be accessed by
-These values can be used by any command that uses global scalar or
+indices 1--6.  These values can be used by any command that uses
-vector values from a compute as input.  See the
+global scalar or vector values from a compute as input.  See the
-:doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
+:doc:`Howto output <Howto_output>` page for an overview of LAMMPS
-options.
+output options.
 
 The scalar value calculated by this compute is "intensive".  The
 vector values are "extensive".
 
-The scalar value will be in temperature :doc:`units <units>`.
+The scalar value is in temperature :doc:`units <units>`.  The vector
-The vector values will be in energy :doc:`units <units>`.
+values are in energy :doc:`units <units>`.
 
 Restrictions
 """"""""""""

doc/src/compute_temp_region_eff.rst

@@ -32,32 +32,33 @@ temperature (e.g., :doc:`thermo_modify <thermo_modify>`).
 
 The operation of this compute is exactly like that described by the
 :doc:`compute temp/region <compute_temp_region>` command, except that
-the formula for the temperature itself includes the radial electron
+the formulas for the temperature (scalar) and diagonal components of
-velocity contributions, as discussed by the
+the symmetric tensor (vector) include the radial electron velocity
-:doc:`compute temp/eff <compute_temp_eff>` command.
+contributions, as discussed by the :doc:`compute temp/eff
+<compute_temp_eff>` command.
 
 Output info
-"""""""""""
+""""""""""
 
 This compute calculates a global scalar (the temperature) and a global
-vector of length 6 (KE tensor), which can be accessed by indices 1--6.
+vector of length 6 (symmetric tensor), which can be accessed by
-These values can be used by any command that uses global scalar or
+indices 1--6.  These values can be used by any command that uses
-vector values from a compute as input.  See the
+global scalar or vector values from a compute as input.  See the
-:doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
+:doc:`Howto output <Howto_output>` page for an overview of LAMMPS
-options.
+output options.
 
 The scalar value calculated by this compute is "intensive".  The
 vector values are "extensive".
 
-The scalar value will be in temperature :doc:`units <units>`.  The
+The scalar value is in temperature :doc:`units <units>`.  The vector
-vector values will be in energy :doc:`units <units>`.
+values are in energy :doc:`units <units>`.
 
 Restrictions
 """"""""""""
 
-This compute is part of the EFF package.  It is only enabled if
+This compute is part of the EFF package.  It is only enabled if LAMMPS
-LAMMPS was built with that package.
+was built with that package.  See the :doc:`Build package
-See the :doc:`Build package <Build_package>` page for more info.
+<Build_package>` page for more info.
 
 Related commands
 """"""""""""""""

doc/src/compute_temp_rotate.rst

@@ -43,12 +43,17 @@ where KE is the total kinetic energy of the group of atoms (sum of
 :math:`N` is the number of atoms in the group, :math:`k_B` is the Boltzmann
 constant, and :math:`T` is the absolute temperature.
 
-A kinetic energy tensor, stored as a six-element vector, is also calculated by
+A symmetric tensor, stored as a six-element vector, is also calculated
-this compute for use in the computation of a pressure tensor.  The formula for
+by this compute for use in the computation of a pressure tensor by the
-the components of the tensor is the same as the above formula, except that
+:doc:`compute pressue <compute_pressure>` command.  The formula for
-:math:`v^2` is replaced by :math:`v_x v_y` for the :math:`xy` component, and
+the components of the tensor is the same as the above expression for
-so on.  The six components of the vector are ordered :math:`xx`, :math:`yy`,
+:math:`E_\mathrm{kin}`, except that the 1/2 factor is NOT included and
-:math:`zz`, :math:`xy`, :math:`xz`, :math:`yz`.
+the :math:`v_i^2` is replaced by :math:`v_{i,x} v_{i,y}` for the
+:math:`xy` component, and so on.  Note that because it lacks the 1/2
+factor, these tensor components are twice those of the traditional
+kinetic energy tensor.  The six components of the vector are ordered
+:math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`,
+:math:`yz`.
 
 The number of atoms contributing to the temperature is assumed to be
 constant for the duration of the run; use the *dynamic* option of the
@@ -80,17 +85,16 @@ Output info
 """""""""""
 
 This compute calculates a global scalar (the temperature) and a global
-vector of length 6 (KE tensor), which can be accessed by indices 1-6.
+vector of length 6 (symmetric tensor), which can be accessed by
-These values can be used by any command that uses global scalar or
+indices 1-6.  These values can be used by any command that uses global
-vector values from a compute as input.  See the
+scalar or vector values from a compute as input.  See the :doc:`Howto
-:doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
+output <Howto_output>` page for an overview of LAMMPS output options.
-options.
 
 The scalar value calculated by this compute is "intensive".  The
 vector values are "extensive".
 
-The scalar value will be in temperature :doc:`units <units>`.  The
+The scalar value is in temperature :doc:`units <units>`.  The vector
-vector values will be in energy :doc:`units <units>`.
+values are in energy :doc:`units <units>`.
 
 Restrictions
 """"""""""""

doc/src/compute_temp_sphere.rst

@@ -77,6 +77,18 @@ tensor is the same as the above formulas, except that :math:`v^2` and
 vector are ordered :math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`,
 :math:`xz`, :math:`yz`.
 
+A symmetric tensor, stored as a six-element vector, is also calculated
+by this compute for use in the computation of a pressure tensor by the
+:doc:`compute pressue <compute_pressure>` command.  The formula for
+the components of the tensor is the same as the above expression for
+:math:`E_\mathrm{kin}`, except that the 1/2 factor is NOT included and
+the :math:`v_i^2` and :math:`\omega^2` are replaced by :math:`v_x v_y`
+and :math:`\omega_x \omega_y` for the :math:`xy` component, and so on.
+Note that because it lacks the 1/2 factor, these tensor components are
+twice those of the traditional kinetic energy tensor.  The six
+components of the vector are ordered :math:`xx`, :math:`yy`,
+:math:`zz`, :math:`xy`, :math:`xz`, :math:`yz`.
+
 The number of atoms contributing to the temperature is assumed to be
 constant for the duration of the run; use the *dynamic* option of the
 :doc:`compute_modify <compute_modify>` command if this is not the case.
@@ -117,17 +129,17 @@ Output info
 """""""""""
 
 This compute calculates a global scalar (the temperature) and a global
-vector of length 6 (KE tensor), which can be accessed by indices 1--6.
+vector of length 6 (symmetric tensor), which can be accessed by
-These values can be used by any command that uses global scalar or
+indices 1--6.  These values can be used by any command that uses
-vector values from a compute as input.
+global scalar or vector values from a compute as input.  See the
-See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS
+:doc:`Howto output <Howto_output>` page for an overview of LAMMPS
 output options.
 
 The scalar value calculated by this compute is "intensive".  The
 vector values are "extensive".
 
-The scalar value will be in temperature :doc:`units <units>`.  The
+The scalar value is in temperature :doc:`units <units>`.  The vector
-vector values will be in energy :doc:`units <units>`.
+values are in energy :doc:`units <units>`.
 
 Restrictions
 """"""""""""

doc/src/compute_viscosity_cos.rst

@@ -86,12 +86,17 @@ where KE is the total kinetic energy of the group of atoms (sum of
 :math:`N` is the number of atoms in the group, :math:`k_B` is the Boltzmann
 constant, and :math:`T` is the absolute temperature.
 
-A kinetic energy tensor, stored as a six-element vector, is also
+A symmetric tensor, stored as a six-element vector, is also calculated
-calculated by this compute for use in the computation of a pressure
+by this compute for use in the computation of a pressure tensor by the
-tensor. The formula for the components of the tensor is the same as
+:doc:`compute pressue <compute_pressure>` command.  The formula for
-the above formula, except that :math:`v^2` is replaced by :math:`v_x v_y` for
+the components of the tensor is the same as the above expression for
-the :math:`xy` component, and so on. The six components of the vector are
+:math:`E_\mathrm{kin}`, except that the 1/2 factor is NOT included and
-ordered :math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`, :math:`yz`.
+the :math:`v_i^2` is replaced by :math:`v_{i,x} v_{i,y}` for the
+:math:`xy` component, and so on.  Note that because it lacks the 1/2
+factor, these tensor components are twice those of the traditional
+kinetic energy tensor.  The six components of the vector are ordered
+:math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`,
+:math:`yz`.
 
 The number of atoms contributing to the temperature is assumed to be
 constant for the duration of the run; use the *dynamic* option of the
@@ -126,21 +131,21 @@ Output info
 """""""""""
 
 This compute calculates a global scalar (the temperature) and a global
-vector of length 7, which can be accessed by indices 1--7.
+vector of length 7, which can be accessed by indices 1--7.  The first
-The first six elements of the vector are the KE tensor,
+six elements of the vector are those of the symmetric tensor discussed
-and the seventh is the cosine-shaped velocity amplitude :math:`V`,
+above.  The seventh is the cosine-shaped velocity amplitude :math:`V`,
-which can be used to calculate the reciprocal viscosity, as shown in the example.
+which can be used to calculate the reciprocal viscosity, as shown in
-These values can be used by any command that uses global scalar or
+the example.  These values can be used by any command that uses global
-vector values from a compute as input.
+scalar or vector values from a compute as input.  See the :doc:`Howto
-See the :doc:`Howto output <Howto_output>` page for an overview of LAMMPS output options.
+output <Howto_output>` page for an overview of LAMMPS output options.
 
 The scalar value calculated by this compute is "intensive".  The
 first six elements of vector values are "extensive",
 and the seventh element of vector values is "intensive".
 
-The scalar value will be in temperature :doc:`units <units>`.
+The scalar value is in temperature :doc:`units <units>`.  The first
-The first six elements of vector values will be in energy :doc:`units <units>`.
+six elements of vector values are in energy :doc:`units <units>`.  The
-The seventh element of vector value will be in velocity :doc:`units <units>`.
+seventh element of vector value us in velocity :doc:`units <units>`.
 
 Restrictions
 """"""""""""