The Coleman-Noll inequality in thermodynamics

Abstract

It is shown that the fundamental inequality used to define a local state of thermal equilibrium by Coleman and Noll (see Arch. Rat. Mech. Anal., vol.4, p.91 of 1959) in their theory of thermostatics of continua is wrong. The variation of states employed in it does not exclude states connected by symmetry transformations to the postulated state of thermal equilibrium. For such states the inequality must be an equality. This error is especially important for a material whose symmetry (isotropy) group is continuous, such as a simple fluid and an isotropic material. The proofs of three theorems given by Coleman and Noll are, as a result, invalid. These theorems essentially state that the pressure of a fluid must be positive, and that for isotropic materials 'the greater stretch will occur in the direction of the greater force'.