fix docs

Author: mrbuche

statmechcrack/monte_carlo.py

@@ -351,9 +351,13 @@ def beta_A_isometric_monte_carlo(self, v, **kwargs):
             \beta\Delta A(v) =
             -\ln\left\langle e^{-\beta\Delta A_0} \right\rangle_\star,
 
-        where :math:`\Delta A_0\equiv
-            A_0(v,\boldsymbol{\lambda})-A_0(1,\boldsymbol{\lambda})`
-        and
+        where the relative free energy of the reference system is
+
+    .. math::
+        \Delta A_0\equiv
+            A_0(v,\boldsymbol{\lambda})-A_0(1,\boldsymbol{\lambda}),
+
+        and where the isometric ensemble average here is
 
         .. math::
             \left\langle \phi \right\rangle_\star \equiv
@@ -365,8 +369,11 @@ def beta_A_isometric_monte_carlo(self, v, **kwargs):
             }
             ,
 
-        where :math:`A_\star(\boldsymbol{\lambda})\equiv
-            A_0(1,\lambda}) + U_1(\boldsymbol{\lambda})`.
+        where the free energy measure here is
+
+    .. math::
+        A_\star(\boldsymbol{\lambda})\equiv
+            A_0(1,\lambda}) + U_1(\boldsymbol{\lambda}).
 
         Args:
             v (array_like): The nondimensional end separation.
@@ -435,9 +442,13 @@ def beta_G_isotensional_monte_carlo(self, p, **kwargs):
             \beta\Delta G(v) =
             -\ln\left\langle e^{-\beta\Delta G_0} \right\rangle_\star,
 
-        where :math:`\Delta G_0\equiv
-            G_0(p,\boldsymbol{\lambda})-G_0(0,\boldsymbol{\lambda})`
-        and
+        where the relative free energy of the reference system is
+
+        .. math::
+        \Delta G_0\equiv
+            G_0(p,\boldsymbol{\lambda})-G_0(0,\boldsymbol{\lambda}),
+
+        and where the isotensional ensemble average here is
 
         .. math::
             \left\langle \phi \right\rangle_\star \equiv
@@ -449,8 +460,11 @@ def beta_G_isotensional_monte_carlo(self, p, **kwargs):
             }
             ,
 
-        where :math:`G_\star(\boldsymbol{\lambda})\equiv
-            G_0(0,\lambda}) + U_1(\boldsymbol{\lambda})`.
+        where the free energy measure here is
+
+        .. math::
+        G_\star(\boldsymbol{\lambda})\equiv
+            G_0(0,\lambda}) + U_1(\boldsymbol{\lambda}).
 
         Args:
             p (array_like): The nondimensional end force.
@@ -520,7 +534,7 @@ def k_isometric_monte_carlo(self, v, **kwargs):
         of the ensemble average
 
         .. math::
-            k \propto
+            \frac{k(v)}{k(1)} =
                 \frac{\left\langle
                     e^{-\beta\Delta A_0^\ddagger}
                 \right\rangle_\star^\ddagger}{\left\langle
@@ -615,7 +629,7 @@ def k_isotensional_monte_carlo(self, p, **kwargs):
         of the ensemble average
 
         .. math::
-            k \propto
+            \frac{k(p)}{k(0)} =
                 \frac{\left\langle
                     e^{-\beta\Delta G_0^\ddagger}
                 \right\rangle_\star^\ddagger}{\left\langle