Hamiltonian Derivations of the Generalized Jarzynski Equalities under Feedback Control

TL;DR

This paper derives generalized Jarzynski equalities for classical Hamiltonian systems under feedback control, extending the second law of thermodynamics and nonequilibrium equalities using Hamiltonian dynamics and Liouville's theorem.

Contribution

It introduces a Hamiltonian derivation of generalized Jarzynski equalities incorporating feedback control, expanding theoretical understanding of nonequilibrium thermodynamics.

Findings

Derived generalized Jarzynski equalities using Hamiltonian dynamics.

Extended the second law of thermodynamics to systems with feedback control.

Provided a theoretical framework for feedback-controlled thermodynamic processes.

Abstract

In the presence of feedback control by "Maxwell's demon," the second law of thermodynamics and the nonequilibrium equalities such as the Jarzynski equality need to be generalized. In this paper, we derive the generalized Jarzynski equalities for classical Hamiltonian dynamics based on the Liouville's theorem, which is the same approach as the original proof of the Jarzynski equality [Phys. Rev. Lett. 78, 2690 (1997)]. The obtained equalities lead to the generalizations of the second law of thermodynamics for the Hamiltonian systems in the presence of feedback control.