Title: Connecting Thermodynamics to Statistical Mechanics in the Strong System-environment Coupling Regime
Abstract: Stochastic thermodynamics describes how the first and second laws of thermodynamics "scale down" to microscopic systems of interest. In this field, and in textbook discussions, it is customary to use the canonical ensemble to represent the equilibrium state of a system that is in contact with a thermal reservoir. Familiar macroscopic relations between internal energy, entropy, free energy, heat and work are easily derived from the canonical distribution. It is known, however, that the canonical ensemble does not accurately describe a nanoscale system that is strongly coupled to its surroundings, such as a biomolecule in aqueous solution. The usual connection between thermodynamics and statistical mechanics cannot easily be invoked in this situation.
I will discuss a modified thermodynamic framework that describes a classical system of interest of arbitrary size that is strongly coupled to its thermal environment. Seven key thermodynamic quantities - internal energy, entropy, volume, enthalpy, Gibbs free energy, heat, and work - are defined microscopically within this framework. These quantities obey thermodynamic relations including both the first and second law, and they satisfy nonequilibrium fluctuation theorems. Additionally, these key quantities scale up to their macroscopic values when the system of interest is large. Thus a unifying framework is developed, which encompasses microscopic, stochastic thermodynamics at one end, and traditional macroscopic thermodynamics at the other. A central element in this approach is a thermodynamic definition of the volume of the system of interest, which converges to the usual geometric definition when the system is large.