Abstract
Assuming time-scale separation, a simple and unified theory of thermodynamics and stochastic thermodynamics is constructed for small classical systems strongly interacting with their environments in a controllable fashion. The total Hamiltonian is decomposed into a bath part and a system part, the latter being the Hamiltonian of mean force. Both the conditional equilibrium of the bath and the reduced equilibrium of the system are described by canonical ensemble theories with respect to their own Hamiltonians. The bath free energy is independent of the system variables and the control parameter. Furthermore, the weak coupling theory of stochastic thermodynamics becomes applicable almost verbatim, even if the interaction and correlation between the system and its environment are strong and varied externally. We further discuss a simple scenario where the present theory fits better with the common intuition about system entropy and heat.
Highlights
One of the most significant discoveries of statistical physics in the past few decades is that thermodynamic variables can be defined on the level of the dynamic trajectory [1,2,3]
We have demonstrated that the usual theory of strong coupling thermodynamics and stochastic thermodynamics, which is based on the assumption of weak coupling between the system and its environment, can be made applicable in the strong coupling regime, if we define the Hamiltonian of mean force as the system Hamiltonian
The present work can be understood as a reinterpretation, synthesis, and simplification of various previous theories of strong coupling stochastic thermodynamics
Summary
One of the most significant discoveries of statistical physics in the past few decades is that thermodynamic variables can be defined on the level of the dynamic trajectory [1,2,3]. The main purpose of this paper is to show that, with TSS and the ensuing conditional equilibrium of bath variables, a much simpler thermodynamic theory can be developed for strongly coupled small classical systems. Entropy, and energy all retain the same definitions and the same physical meanings as in the weak coupling theory, as long as the bath entropy understood as conditioned on the system state. In a complementary paper [38], two of us develop a theory of stochastic thermodynamics using nonlinear Ito-Langevin dynamics, establish its covariance property, and derive the Crooks fluctuation theorem, Jarzynsk equality, and Clausius inequality. Riemannian manifold x, whereas in this paper, we consider Hamiltonian systems with Liouville measure i d pidqi.) The combination of these two works provides a covariant theory of thermodynamics and stochastic thermodynamics for systems strongly interacting with a single heat bath, with TSS as the only assumption.
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