Some inequalities in the fidelity approach to phase transitions

TL;DR

This paper explores the fidelity approach to phase transitions, establishing bounds on fidelity susceptibility using thermodynamic quantities and linking fidelity to nonequilibrium work via the Jarzynski equality.

Contribution

It introduces bounds on fidelity susceptibility in phase transitions and connects fidelity with nonequilibrium work, expanding the theoretical framework.

Findings

Bounds on fidelity susceptibility expressed in thermodynamic terms

Relation between fidelity and nonequilibrium work via Jarzynski equality

Applicability to both commutative and noncommutative cases

Abstract

We present some aspects of the fidelity approach to phase transitions based on lower and upper bounds on the fidelity susceptibility that are expressed in terms of thermodynamic quantities. Both commutative and non commutative cases are considered. In the commutative case, in addition, a relation between the fidelity and the nonequilibrium work done on the system in a process from an equilibrium initial state to an equilibrium final state has been obtained by using the Jarzynski equality.