On entropy production and energy loss

Paolo Podio-Guidugli

Accademia dei Lincei e Università di Roma Tor Vergata

In a 1996 paper appeared in Meccanica, Jim Serrin summarized and completed his views about the format of the basic laws of continuum mechanics. Starting from suitable weak forms of the postulates about cyclic processes of classic thermodynamics of homogeneous processes, he showed how the two state functions of importance, internal energy and entropy, could be consistently constructed for a fairly general and representative constitutive class of materials; moreover, he proved that the standard dissipation inequality that filters unphysical constitutive prescriptions à la Coleman-Noll could be arrived at also by replacing the usual internal energy equation by an imbalance law under form of an inequality. In so doing, he implied that not only, as is customary, the internal source of entropy should be taken positive, but also that the non-constitutively specified part of the internal source of internal energy should be taken negative: in other words, that entropy production should be accompanied by energy loss. In my talk, I shall show how a careful hybridization of statistical and continuum mechanics leads to identifying those internal sources as purely kinetic macroscopic consequences of microscopic motion randomness, consequences that continuum mechanics alone could not predict.