Stochastic and Macroscopic Thermodynamics of Strongly Coupled Systems

We develop a thermodynamic framework that describes a classical system of interest S that is strongly coupled to its thermal environment E. Within this framework, seven key thermodynamic quantitiesinternal energy, entropy, volume, enthalpy, Gibbs free energy, heat, and work-are defined microscopically. These quantities obey thermodynamic relations including both the first and second law, and they satisfy nonequilibrium fluctuation theorems. We additionally impose a macroscopic consistency condition: When S is large, the quantities defined within our framework scale up to their macroscopic counterparts. By satisfying this condition, we demonstrate that a unifying framework can be developed, which encompasses both stochastic thermodynamics at one end, and macroscopic thermodynamics at the other. A central element in our approach is a thermodynamic definition of the volume of the system of interest, which converges to the usual geometric definition when S is large. We also sketch an alternative framework that satisfies the same consistency conditions. The dynamics of the system and environment are modeled using Hamilton's equations in the full phase space.