First and Second Law of Thermodynamics at strong coupling

TL;DR

This paper extends thermodynamic laws to strongly coupled small driven systems, demonstrating that energy and heat can be defined consistently, leading to fluctuation theorems and second law implications without initial uncorrelated states.

Contribution

It introduces a Hamiltonian framework for defining heat and energy in strongly coupled systems, avoiding initial state assumptions and clarifying conditions for experimental measurement.

Findings

Total entropy production obeys an integral fluctuation theorem.

The first and second laws are valid without assuming initial uncorrelated states.

Conditions for unique and measurable heat definitions are established.

Abstract

For a small driven system coupled strongly to a heat bath, internal energy and exchanged heat are identified such that they obey the usual additive form of the first law. By identifying this exchanged heat with the entropy change of the bath, the total entropy production is shown to obey an integral fluctuation theorem on the trajectory level implying the second law in the form of a Clausius inequalilty on the ensemble level. In this Hamiltonian approach, the assumption of an initially uncorrelated state is not required. The conditions under which the proposed identification of heat is unique and experimentally accessible are clarified.