Synopsis: Creating—or destroying—entropy in a small system

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Illustration: Alan Stonebraker

Entropy production theorems and some consequences

Arnab Saha, Sourabh Lahiri, and A. M. Jayannavar

Published July 14, 2009

The second law of thermodynamics forbids a decrease in entropy of an isolated system. However, in statistical mechanics this strict prohibition is softened to a probabilistic statement, which allows transient decreases in entropy to occur with a small probability. The likelihood of such fluctuations is vanishingly small in macroscopic bodies, but in smaller systems, such as a stretched DNA molecule, they can actually be observed.

This possibility has motivated recent work on fluctuation theorems, which compare the probability of a system reducing its entropy (over short times) in out-of-equilibrium processes to those in which the entropy increases. In a paper appearing in Physical Review E, Arnab Saha of the S. N. Bose National Center For Basic Sciences in Kolkata, India, and Sourabh Lahiri and Arun Jayannavar, of the Institute of Physics, in Bhubaneswar, India, build on this work and study the total entropy produced in a simple system that is driven out of equilibrium. They model a Brownian particle in a harmonic trap and consider the change in entropy when a time-dependent external force is applied to the particle, or the trap itself is moved in an arbitrary manner.

In nonequilibrium steady states, the detailed fluctuation theorem relates the probabilities of observing entropy changes of equal magnitude but opposite sign. Saha et al. show, somewhat surprisingly, that the Brownian particles also obey this theorem even in the nonstationary, transient regime, provided the system is prepared in equilibrium.

These and other advances given in this paper should stimulate the analysis of thermal fluctuations in small systems, and their application in determining free energy differences. – Ron Dickman

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