Second Law and Its Amendment: The Axiom of No-Reversible Directions Revisited

A toy model is used to describe the following steps to achieve the no-reversible-direction axiom in a tutorial manner: (i) choose a state space results in the balance equations on state space which are linear in the process directions, (ii) avoid a reversible process direction that cannot be generated via a combination of non-reversible ones, (iii) process directions that are in the kernel of the balance equations and do not enter the entropy production. The Coleman–Mizel formulation of the second law and the Liu relations follow immediately.