Dynamic dependence of nonequilibrium work limits the validity of the Jarzynski Equality

TL;DR

This paper critically examines the limits of the Jarzynski equality in nonequilibrium thermodynamics, showing it does not hold universally and depends on the dynamics of the work protocol, especially in finite or non-quasi-static processes.

Contribution

It demonstrates that the Jarzynski equality is valid only under specific conditions and highlights the dependence of work on the protocol's dynamics, challenging its universal applicability.

Findings

JE holds only for isothermal transformations

Work depends on the protocol's speed and dynamics

In adiabatic limits, work equals change in internal energy

Abstract

The Jarzynski equality (JE) is analyzed in regard to its validity for both quasi-static transformations in the thermodynamic limit and Hamiltonian evolutions of the work protocol. In the first case, we show that the JE holds for isothermal transformations only; in the second case, we show that the work done (linked to the final state Hamiltonian) depends on the temporal dynamics of the work protocol (including its speed), thus precluding the possibility of identifying it with the free energy or any other thermodynamic state function. Even in the case of thermodynamic limit and infinitesimally slow transformations of the Hamiltonian (adiabatic invariance) following states of thermodynamic equilibrium, the resulting work expression does not default to the JE, but to the work relation for adiabatic thermodynamic transformations, W=Delta U, where W is work and U is internal energy.