Thermodynamics of small systems with emergent structures

Jan Korbel, Simon David Lindner, Rudolf Hanel, Stefan Thurner

Published 2020-04-14Version 1

We derive the entropy for a closed system of particles that can form structures, molecules in the simplest case. The entropy differs from the Boltzmann-Gibbs entropy by a term that captures the molecule states. For large systems the approach is equivalent to the grand canonical ensemble. For small systems large molecules start to play a dominant role. The number of molecules becomes a key quantity and appears explicitly in the second law of thermodynamics and in fluctuation theorems. We show that the fully connected Ising model with emergent structures exhibits a first-order phase transition.