Entropy, free energy, work, and other thermodynamic variables in economics

Contrary to recent work by Gillett, it is entropy change, not free energy change, which in general determines the direction of spontaneous change both of isolated thermodynamic systems and nonisolated subsystems of isolated thermodynamic systems. This is formally shown here, in a proof that allows the heat evolved from a chemical reaction to be (partially) turned into work. Due to Gibbs' equivalence of energy minimization and entropy maximization, entropy maximization can actually be used to characterize the equilibrium of all thermodynamic systems. Next, it is shown that changes in free energy as traditionally defined are not, in general, related to the amount of work a system can perform (although they are so related in special cases). Even if free energy were always related to the work a system can perform, the “work a system can perform” is not related to economic value. Hence it is unclear how free energy could have any economic importance. This in turn confirms much (though not all) of what past authors in ecological economics have written about the importance of the entropy law for economics.