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Duration of Local Violations of the Second Law of Thermodynamics Along Single Trajectories in Phase Space by García-García, Reinaldo; Domínguez, Daniel is a scholarly article available to read on EtoBox.

What is Duration of Local Violations of the Second Law of Thermodynamics Along Single Trajectories in Phase Space about?

We define the {\it violation fraction} $\nu$ as the cumulative fraction of time that the entropy change is negative during single realizations of processes in phase space. This quantity depends both on the number of degrees of freedom $N$ and the duration of the time interval $\tau$. In the large-$\tau$ and large-$N$ limit we show that, for ergodic and microreversible systems, the mean value of $\nu$ scales as $\langle\nu(N,\tau)\rangle\sim\big(\tau N^{\frac{1}{1+\alpha}}\big)^{-1}$. The exponent $\alpha$ is positive and generally depends on the protocol for the external driving forces, being $\alpha=1$ for a constant drive. As an example, we study a nontrivial model where the fluctuations of the entropy production are non-Gaussian: an elastic line driven at a constant rate by an anharmonic trap. In this case we show that the scaling of $\langle \nu \rangle$ with $N$ and $\tau$ agrees with our result. Finally, we discuss how this scaling law may break down in the vicinity of a continuous phase transition.

Author

García-García, Reinaldo; Domínguez, Daniel

Published

2012

Language

EN