Development and regression of a large fluctuation

Abstract

We study the evolution leading to (or regressing from) a large fluctuation in a Statistical Mechanical system. We introduce and study analytically a simple model of many identically and independently distributed microscopic variables $n_m$ ($m=1,M$) evolving by means of a master equation. We show that the process producing a non-typical fluctuation with a value of $N={\sum }_{m=1}^M{n}_m$ well above the average $⟨N⟩$ is slow. Such process is characterized by the power-law growth of the largest possible observable value of $N$ at a given time $t$. We find similar features also for the reverse process of the regression from a rare state with $N\gg ⟨N⟩$ to a typical one with $N\simeq ⟨N⟩$.

19 pages, 6 figures. To appear on Physical Review E

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