Tracing the classical molecular nature of entropy generation

Abstract

The second law of thermodynamics and the concept of positive entropy generation are analyzed following classical statistical mechanics methods. Previously, using the generalized Boltzmann–Gibbs entropy and its associated general entropy conservation relation, positive entropy generation expressions were obtained in agreement with phenomenological results and the work of Boltzmann and Gibbs. In this study, using the general approach, we formally and explicitly trace the specific entropy generation expressions to truncations in the full N-body description of the entropy state to a lower s-body description. Using higher-order superposition approximations, it is formally shown that the generalized Boltzmann–Gibbs entropy in the s-order state is always less than the corresponding Boltzmann–Gibbs entropy in the lower (s − 1)-order state. Using the general form of the entropy conservation equation, entropy generation is shown to be a required compensatory effect to ensure that all physical variables and physical processes associated with heat, work, temperature, etc., are independent of the particular entropy definition state.