A thermodynamic conundrum through the ages

Abstract

Recently, in a series of three papers, Tolley, Woodfield, and Hansen analyzed six types of spontaneous ideal processes where $Q=W=0$ and for which $\Delta U$ and $\Delta S$ are also zero. But this leads to a conundrum because it does not answer the question why the process occurs spontaneously, and where the entropic increase originated from. The papers resolve an apparent contradiction in classical thermodynamics that was recognized by Max Planck in his famous Treatise on Thermodynamics a century ago. Planck realized the need for inclusion of the distribution of matter in a more complete development of thermodynamics. However no such development was forthcoming. The conundrum is resolved by Hansen and colleagues by the novel proposal of a probability distribution of particles, and an entropy change associated with this distribution, $\Delta S_D$. Equations for $\Delta S_D$ have been worked out for the six types of processes considered. Applications of their fundamental work to efficient energy conversion in real chemical and biological systems—that presents new challenges and conundrums—and intersects with the author’s own research are discussed, and some suggestions for future work are offered.