A Note on Non-equilibrium Work Fluctuations and Equilibrium Free Energies

Abstract

We consider in this paper, a few important issues in non-equilibrium work fluctuations and their relations to equilibrium free energies. First we show that Jarzynski identity can be viewed as a cumulant expansion of work. For a switching process which is nearly quasistatic the work distribution is sharply peaked and Gaussian. We show analytically that dissipation given by average work minus reversible work $W_R$, decreases when the process becomes more and more quasistatic. Eventually, in the quasistatic reversible limit, the dissipation vanishes. However estimate of $p$ - the probability of violation of the second law given by the integral of the tail of the work distribution from $-\infty$ to $W_R$, increases and takes a value of $0.5$ in the quasistatic limit. We show this analytically employing Gaussian integrals given by error functions and Callen-Welton theorem that relates fluctuations to dissipation in process that is nearly quasistatic. Then we carry out Monte Carlo simulation of non-equilibrium processes in a liquid crystal system in the presence of an electric field and present results on reversible work, dissipation, probability of violation of the second law and distribution of work

15 pages, 4 figures

References in corpus (3)

• Path ensembles averages in systems driven far-from-equilibrium
• Distribution of work in isothermal non-equilibrium processes
• Thermodynamics as a nonequilibrium path integral

Cited by in corpus (1)

• Toward the nonequilibrium thermodynamic analog of complexity and the Jarzynski identity