Continuum thermodynamics based on a notion of rate of loss of information

Abstract

It is not known for sure how to formulate the second law so as to describe adequately the behaviour of bodies which deform and remember the past. Following the lead of COLEMAN & NOLL 1 it has become common practice in continuum mechanics to take as the second law the proposition that the Clausius-Duhem inequality holds in every process compatible with the balance of mass, momentum, moment of momentum and energy. Interpreted in that way the law leads to restrictions on constitutive relations, and COLEMAN & NOLL developed a method for determining those res t r i c t ions -a method which has been extended, elaborated and applied by many. 2 To take the second law to be the Clausius-Duhem inequality is to assume, among other things, that temperature and entropy are defined far from equilibrium. Those who do not find the truth of that assumption transparently obvious ask for an alternative approach and my intention is to propose one tentatively. The future behaviour of a body is determined by prescribing initial data, which may well include information about its past history, and also the action of the external world by way of surface traction and body forces and the supply of heat through conduction and radiation. The action of the external world may be such that only certain gross features of the initial data remain relevant to predicting the ultimate behaviour whereas the details become less and less relevant. Thus a homogeneous, rigid, heat conductor, which is thermally isolated and whose initial temperature field is prescribed, approaches equilibrium at a temperature determined solely by the total initial internal energy and the specific heat of the conductor; all features of the initial temperature other than the total energy ultimately become irrelevant. In statistical mechanics the increasing irrelevance of the details of the initial data is called, not strictly accurately, loss of information and I shall use the same terminology here.