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An Isaac Newton Institute Workshop

Non-Equilibrium Dynamics of Interacting Particle Systems

The fluctuation & nonequilibrium free energy theorems, theory & experiment

27th March 2006

Author: Evans, DJ (Australian National University)

Abstract

1. We give a brief summary of the derivations of the Evans-Searles Fluctuation Theorems (FTs) and the NonEquilibrium Free Energy Theorems (Crooks and Jarzynski). The discussion is given for time reversible Newtonian dynamics. We emphasize the role played by thermostatting. We also highlight the common themes inherent in the Fluctuation and Free Energy Theorems. We discuss a number of simple consequences of the Fluctuation Theorems including the Second Law Inequality, the Kawasaki Identity and the fact that the dissipation function which is the subject of the FT, is a nonlinear generalization of the spontaneous entropy production, that is so central to linear irreversible thermodyanamics. Lastly we give a brief update on the latest experimental tests of the FTs (both steady state and transient) and the NonEquilibrium Free Energy Theorem, using optical tweezer apparatus.

2 The Fluctutation Theorem: In 1993 we discovered a relation, subsequently known as the Fluctuation Theorem (FT), which gives an analytical expression for the probability of observing Second Law violating dynamical fluctuations in small thermostatted nonequilibrium systems which are observed for a short period of time. This Theorem places quantitative restrictions on the operation of small (nano) machines and devices. These constraints cannot be circumvented. Quantitative predictions made by the Fluctuation Theorem regarding the probability of Second Law `violations' have been confirmed experimentally, both using molecular dynamics computer simulation and very recently in two laboratory experiments[1] which employed optical tweezers. In this talk we give a brief summary of the theory [2] and a description of the experiments.

References

[1] Experimental demonstration of violations of the Second Law of Thermodynamics for small systems and short time scales, by Wang, G.M., Sevick, E.M., Mittag, E., Searles, D.J. and Evans, D.J., Phys. Rev. Lett., 89 (5), 050601/1?4 (2002).

[2] The Fluctuation Theorem by Denis J Evans and Debra J Searles, Advances in Physics, 51 , 1529-1585(2002).