On entropy gain and energy loss

At variance with textbook practice in continuum mechanics, which categorises entropy and internal energy as primitive notions, James Serrin showed in his work how to construct those two state functions for a representative constitutive class of Cauchy materials. As for entropy, he derived the standard entropy imbalance law, the Clausius–Duhem inequality; he derived an imbalance law also for the internal energy. These laws may be written as balances, provided suitable internal sources are taken into account, positive for entropy, negative for energy: according to Serrin, both an entropy gain and an energy loss are to be expected; according to the practice in continuum mechanics, it is irrelevant to evaluate that gain, and that loss may safely be taken null. In the present contribution, after a quick recapitulation of Serrin’s view points, I show how the juxtaposition of the treatments of transport phenomena in continuum and statistical mechanics leads to identifying, for whatever Cauchy material, the internal source of energy—Serrin’s energy loss—as a macroscopic consequence of microscopic motion randomness that diminishes progressively when microscopic velocity fluctuations decrease.