Nanothermodynamics: Stable Thermal Equilibrium and Nanoscale Fluctuations

Nanothermodynamics is the theory describing how large systems subdivide into equilibrium distributions of small subsystems. A key ingredient is Hill’s subdivision potential (E) that ensures adherence to the 1st and 2nd laws of thermodynamics in systems of any size. In this review and reassessment, it is emphasized that nanothermodynamics gives new insight into many experiments, theories, and simulations. Measurements establishing the need for nanothermodynamics show thermodynamic heterogeneity from multiple effective temperatures (Ti) inside most types of materials. One theoretical result that requires E=0 is the stable solution of Ising’s original model for finite chains of interacting spins, a solution Ising could not have found 40 years before Hill’s work. Another result is a novel solution to Gibbs’ paradox that makes the entropy of the semiclassical ideal gas exactly extensive, even for small systems. Molecular dynamics simulations reveal how a standard fluctuation relation is modified when local degrees of freedom fluctuate faster than their coupling to the heat bath, consistent with the measured thermodynamic heterogeneity. Simulations of a Creutz-like model, containing Ising spins coupled to an explicit heat bath of Einstein oscillators, are used to study the 2nd law. It is found that maximizing the total entropy (St) requires an intrinsically irreversible step, providing a counterexample to the usual claim that statistical mechanics emerges from reversible dynamics. Furthermore, fluctuations of this model are best described by Einstein’s reversal of Boltzmann’s relation and the 2nd law, not by recent fluctuation theorems.