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

• Published in: arXiv.org
• Main Authors: M Suman Kalyan, Prasad, G Anjan, Sastry, V S S, Murthy, K P N
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 19.11.2010
• Subjects: Computer simulation; Electric fields; Equilibrium; Error functions; Integrals; Liquid crystals; Monte Carlo simulation; Physics - Soft Condensed Matter; Physics - Statistical Mechanics; Variation
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1011.4413

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