Fluctuation Theorems and the Foundations of Statistical Mechanics

Abstract

In 1993 Evans, Cohen and Morriss described the first Fluctuation Theorem1. Fluctuation theorems describe the statistics of time averages of a generalized entropy production, namely the dissipation function. Close to equilibrium the average dissipation function is the average purely irreversible entropy production. However far from equilibrium where the entropy production cannot be defined, the dissipation function remains a precisely defined mathematical quantity. In words, the time average dissipation function Ωt , is the irreversible work performed on a system divided by the ambient thermodynamic temperature. Because the microscopic equations of motion (either classical or quantum mechanical) are always time reversal symmetric, the dissipation function like the entropy production may be positive or negative.