An Amendment to the Second Law

Abstract

A toy-model is used for describing the steps achieving the no-reversibledirection axiom in a tutorial manner: i) choice of a state space results in the balance equations on state space which are linear in the process directions, ii) a reversible process direction cannot be generated by combination of non-reversible ones, iii) process directions which are in the kernel of the balance equations do not enter the entropy production. The Coleman-Mizel formulation of the second law and the Liu relations follow immediately.

Entropy Principle and Recent Results in Non-Equilibrium Theories

“…This is not in contradiction with the amendment to the second law proposed by Muschik and Ehrentraut [14], specified in the the introduction, because that amendment implicitly refers to exact constitutive equations [14,75].…”

“…Moreover, one may ask whether constitutive functions that depend on higher order gradients are compatible with the second law without further conditions, or not. These kind of observations lead to an amendment of the classical formulation of the second law [14], and also to more involved mathematical methods (see Section 5). In order to separate the conditions from the consequences we repeat the previous derivation with the help of Liu procedure.…”

“…First of all, the entropy principle itself, such as formulated by Coleman and Noll, could appear as an arbitrary assumption, since nothing prevents second law of thermodynamics to restrict the processes instead of the constitutive equations. Thus, Muschik and Ehrentraut [14] proposed the following amendment to the second law:…”

Why so many “schools” of thermodynamics?

“…Consequently, an amendment to the second law is needed. This amendment is the no-reversible direction axiom [51]: Except in equilibrium sub-space, reversible process directions in state space do not exist. Using this axiom, a proof of the Coleman-Mizel formulation (63) is possible [5], and the second law is detected to be material selective.…”

“…Liu's Proposition [53,51]: Presupposing the Coleman-Mizel formulation of the 2nd law, the following statement is valid: In large state spaces constitutive equations satisfy the Liu relations…”