Fluctuation theorems and atypical trajectories

Abstract

In this work, we have studied simple models that can be solved analytically\nto illustrate various fluctuation theorems. These fluctuation theorems provide\nsymmetries individually to the distributions of physical quantities like the\nclassical work ($W_c$), thermodynamic work ($W$), total entropy ($\\Delta\ns_{tot}$) and dissipated heat ($Q$), when the system is driven arbitrarily out\nof equilibrium. All these quantities can be defined for individual\ntrajectories. We have studied the number of trajectories which exhibit\nbehaviour unexpected at the macroscopic level. As the time of observation\nincreases, the fraction of such atypical trajectories decreases, as expected at\nmacroscale. Nature of distributions for the thermodynamic work and the entropy\nproduction in nonlinear models may exhibit peak (most probable value) in the\natypical regime without violating the expected average behaviour. However,\ndissipated heat and classical work exhibit peak in the regime of typical\nbehaviour only.\n