From 007f7fbbfb0be8cefcb85126ffdb28ea6500e4e4 Mon Sep 17 00:00:00 2001 From: Karl Hammond Date: Mon, 22 Aug 2022 23:46:49 -0500 Subject: [PATCH] Fixed kT vs k_B T in a couple of places and associated description --- doc/src/compute_fep.rst | 16 ++++++++-------- doc/src/compute_fep_ta.rst | 4 ++-- doc/src/compute_temp_chunk.rst | 8 ++++---- doc/src/compute_temp_profile.rst | 8 ++++---- 4 files changed, 18 insertions(+), 18 deletions(-) diff --git a/doc/src/compute_fep.rst b/doc/src/compute_fep.rst index b87f369137..e2de8d405b 100644 --- a/doc/src/compute_fep.rst +++ b/doc/src/compute_fep.rst @@ -92,9 +92,9 @@ stepwise alchemical transformations during a simulation run: .. math:: - \Delta_0^1 A = \sum_{i=0}^{n-1} \Delta_{\lambda_i}^{\lambda_{i+1}} A = - kT + \Delta_0^1 A = \sum_{i=0}^{n-1} \Delta_{\lambda_i}^{\lambda_{i+1}} A = - k_B T \sum_{i=0}^{n-1} \ln \left< \exp \left( - \frac{U(\lambda_{i+1}) - - U(\lambda_i)}{kT} \right) \right>_{\lambda_i} + U(\lambda_i)}{k_B T} \right) \right>_{\lambda_i} This compute is suitable for the finite-difference thermodynamic integration (FDTI) method :ref:`(Mezei) `, which is based on an @@ -131,9 +131,9 @@ both the forward and reverse routes: .. math:: - \left< \frac{1}{1 + \exp\left[\left(U_1 - U_0 - \Delta_0^1A \right) /kT + \left< \frac{1}{1 + \exp\left[\left(U_1 - U_0 - \Delta_0^1A \right) /k_B T \right]} \right>_0 = \left< \frac{1}{1 + \exp\left[\left(U_0 - U_1 + - \Delta_0^1A \right) /kT \right]} \right>_1 + \Delta_0^1A \right) /k_B T \right]} \right>_1 The value of the free energy difference is determined by numerical root finding to establish the equality. @@ -276,8 +276,8 @@ trajectories during which the volume fluctuates or changes :ref:`(Allen and Tild .. math:: - \Delta_0^1 A = - kT \sum_{i=0}^{n-1} \ln \frac{\left< V \exp \left( - - \frac{U(\lambda_{i+1}) - U(\lambda_i)}{kT} \right) + \Delta_0^1 A = - k_B T \sum_{i=0}^{n-1} \ln \frac{\left< V \exp \left( - + \frac{U(\lambda_{i+1}) - U(\lambda_i)}{k_B T} \right) \right>_{\lambda_i}}{\left< V \right>_{\lambda_i}} ---------- @@ -287,8 +287,8 @@ Output info This compute calculates a global vector of length 3 which contains the energy difference ( :math:`U_1-U_0` ) as c_ID[1], the -Boltzmann factor :math:`\exp(-(U_1-U_0)/kT)`, or -:math:`V \exp(-(U_1-U_0)/kT)`, as c_ID[2] and the +Boltzmann factor :math:`\exp(-(U_1-U_0)/k_B T)`, or +:math:`V \exp(-(U_1-U_0)/k_B T)`, as c_ID[2] and the volume of the simulation box :math:`V` as c_ID[3]. :math:`U_1` is the pair potential energy obtained with the perturbed parameters and :math:`U_0` is the pair potential energy obtained with the diff --git a/doc/src/compute_fep_ta.rst b/doc/src/compute_fep_ta.rst index 504ed6aa23..1fe89194ca 100644 --- a/doc/src/compute_fep_ta.rst +++ b/doc/src/compute_fep_ta.rst @@ -42,7 +42,7 @@ in a single simulation: .. math:: \gamma = \lim_{\Delta \mathcal{A} \to 0} \left( \frac{\Delta A_{0 \to 1 }}{\Delta \mathcal{A}}\right)_{N,V,T} - = - \frac{kT}{\Delta \mathcal{A}} \ln \left\langle \exp\left(\frac{-(U_1 - U_0)}{kT}\right) \right\rangle_0 + = - \frac{k_B T}{\Delta \mathcal{A}} \ln \left\langle \exp\left(\frac{-(U_1 - U_0)}{k_B T}\right) \right\rangle_0 During the perturbation, both axes of *plane* are scaled by multiplying :math:`\sqrt{\mathrm{scale\_factor}}`, while the other axis divided by @@ -62,7 +62,7 @@ Output info This compute calculates a global vector of length 3 which contains the energy difference :math:`(U_1-U_0)` as c_ID[1], the Boltzmann factor -:math:`\exp\bigl(-(U_1-U_0)/kT\bigr)`, as c_ID[2] and the change in the *plane* +:math:`\exp\bigl(-(U_1-U_0)/k_B T\bigr)`, as c_ID[2] and the change in the *plane* area :math:`\Delta \mathcal{A}` as c_ID[3]. :math:`U_1` is the potential energy of the perturbed state and :math:`U_0` is the potential energy of the reference state. The energies include kspace terms if these are diff --git a/doc/src/compute_temp_chunk.rst b/doc/src/compute_temp_chunk.rst index 22c89a3062..f3d1a83351 100644 --- a/doc/src/compute_temp_chunk.rst +++ b/doc/src/compute_temp_chunk.rst @@ -69,11 +69,11 @@ The temperature is calculated by the formula .. math:: - \text{KE} = \frac{\text{DOF}}{2} k T, + \text{KE} = \frac{\text{DOF}}{2} k_B T, where KE is the total kinetic energy of all atoms assigned to chunks (sum of :math:`\frac12 m v^2`), DOF is the the total number of degrees of -freedom for those atoms, :math:`k` is Boltzmann constant, and :math:`T` is the +freedom for those atoms, :math:`k_B` is Boltzmann constant, and :math:`T` is the absolute temperature. The DOF is calculated as :math:`N\times`\ *adof* @@ -107,11 +107,11 @@ formula .. math:: - \text{KE} = \frac{\text{DOF}}{2} k T, + \text{KE} = \frac{\text{DOF}}{2} k_B T, where KE is the total kinetic energy of the chunk of atoms (sum of :math:`\frac12 m v^2`), DOF is the total number of degrees of freedom for all -atoms in the chunk, :math:`k` is the Boltzmann constant, and :math:`T` is the +atoms in the chunk, :math:`k_B` is the Boltzmann constant, and :math:`T` is the absolute temperature. The number of degrees of freedom (DOF) in this case is calculated as diff --git a/doc/src/compute_temp_profile.rst b/doc/src/compute_temp_profile.rst index f429216218..9076a6cb14 100644 --- a/doc/src/compute_temp_profile.rst +++ b/doc/src/compute_temp_profile.rst @@ -81,15 +81,15 @@ each atom, the temperature is calculated by the formula .. math:: \text{KE} = \left( \frac{\text{dim}}{N} - N_s N_x N_y N_z - - \text{extra} \right) \frac{k T}{2}, + - \text{extra} \right) \frac{k_B T}{2}, where KE is the total kinetic energy of the group of atoms (sum of :math:`\frac12 m v^2`; dim = 2 or 3 is the dimensionality of the simulation; :math:`N_s =` 0, 1, 2, or 3 for streaming velocity subtracted in 0, 1, 2, or 3 dimensions, respectively; *extra* is the number of extra degrees of freedom; -*N* is the number of atoms in the group; *k* is the Boltzmann constant, and -*T* is the absolute temperature. The :math:`N_s N_x N_y N_z` term is the -number of degrees of freedom subtracted to adjust for the removal of the +*N* is the number of atoms in the group; :math:`k_B` is the Boltzmann constant, +and :math:`T` is the absolute temperature. The :math:`N_s N_x N_y N_z` term is +the number of degrees of freedom subtracted to adjust for the removal of the center-of-mass velocity in each direction of the *Nx\*Ny\*Nz* bins, as discussed in the :ref:`(Evans) ` paper. The extra term defaults to :math:`\text{dim} - N_s` and accounts for overall conservation of