Quantum Work Relations under Trial Hamiltonians

TL;DR

This paper investigates the accuracy of quantum work relations when systems are driven by trial Hamiltonians instead of the original, deriving inequalities and corrections that quantify the deviation from the ideal relations.

Contribution

It introduces an inequality and correction terms for quantum work relations under trial Hamiltonians, extending the Bogoliubov inequality to quantum free energy differences.

Findings

Derived an inequality for quantum work relations with trial Hamiltonians

Expressed correction terms as averages of Hamiltonian differences

Generalized the Bogoliubov inequality for quantum free energy differences

Abstract

The universal quantum work relation connects a functional of an arbitrary observable averaged over the forward process to the free energy difference and another functional averaged over the time-reversed process. Here, we ask the question if the system is driven out of equilibrium by a different Hamiltonian rather than the original one during the forward process and similarly during the reversed process then how accurate is the quantum work relation. We present an inequality that must be satisfied when the system is driven out by such a trial Hamiltonian. This also answers the issue of accuracy of the Jarzynski relation with a trial Hamiltonian. We have shown that the correction term can be expressed as the averages of the difference operator between the accurate and trial Hamiltonians. This leads to a generalized version of the Bogoliubov inequality for the free energy differences.