Before revision:  The ensemble of proteins attains the equilibrium, \psi_N= \psi_N ^{eq, where the average of \Delta \psi}  _{ N } over fixed mutants is equal to zero. Approximating the probability density function (PDF) of \Delta \psi_N by a log-normal distribution, the PDF of \Delta \psi _{N (\simeq \Delta\Delta \psi_{ND}) in fixed mutants is estimated.
After revision:  The ensemble of proteins attains the equilibrium, \psi_N= \psi_N ^{eq, where the average of \Delta \psi} _{ N } are estimated with reasonable values for 14 protein domains. In addition, approximating the probability density function (PDF) of \Delta \psi_N by a log-normal distribution, the PDF of \Delta \psi _{N (\simeq \Delta\Delta \psi_{ND}) in fixed mutants is estimated.