Equilibrium States

Abstract

This chapter examines the equilibrium states of a body in a given environment. The heating conditions are trivially satisfied and the question reduces to examining the conditions of mechanical equilibrium. As a general consequence of the latter, the Eshelby conservation law for the bulk matter will be derived. Then the conditions are given a variational form: the first variations of certain functionals vanish in the equilibrium states. The origin of this fact is deep: these functionals involve the entropy; the variational principles are ultimately related to the second law of thermodynamics. That the first variations vanish is a necessary condition for an extremum, but unstable equilibrium states, admitted by the definition of an equilibrium state, do not correspond to extrema. In this chapter only the first variations will be examined. The extrema, the second variations, and their relation to the stability will be treated in the next chapter.