On the kinetic meaning of the second law of thermodynamics

Abstract

A kinetic‐molecular theory which connects dissipation and fluctuations is used to examine the second law of thermodynamics. Considerations are restricted to systems with stable equilibrium states and are based on a conservation condition satisfied by transport processes which obey microscopic reversibility. The conservation condition leads to a statement about the accessibility of equilibrium states which is comparable to the Carathéodory statement of the second law. Insofar as the transport of heat into a system is the only process which violates microscopic reversibility, this statement is equivalent to the second law. The present treatment also gives a simple kinetic proof of the Clausius inequalities T_RdS/dt?dQ/dt and dS/dt?0 for the entropy. Using the statistical aspects of the fluctuation–dissipation postulates, a class of state functions related to the equilibrium statistical distribution are defined, and it is verified that the entropy is one of these functions. A brief discussion is given of how to extend these results to systems with multiple phases or at nonequilibrium steady states.