Jarzynski Equality for an Energy-Controlled System (Proceedings of nanoPHYS'11)

TL;DR

This paper extends the Jarzynski equality to systems with controllable energy, enabling entropy difference calculations through artificial dynamics, with potential applications in optimization problems.

Contribution

It introduces a novel extension of the Jarzynski equality for energy-controlled systems using artificial dynamics, facilitating entropy computations.

Findings

Derived an exact identity for energy-controlled nonequilibrium processes.

Proposed a practical method for entropy difference estimation.

Suggested applications in optimization problems.

Abstract

We extend the Jarzynski equality, which is an exact identity between the equilibrium and nonequilibrium averages, to be useful to compute the value of the entropy difference by changing the Hamiltonian. To derive our result, we introduce artificial dynamics where the instantaneous value of the energy can be arbitrarily controlled during a nonequilibrium process. We establish an exact identity on such a process corresponding to the so-called Jarzynski equality. It is suggested that our formulation is valuable in a practical application as in optimization problems.