Microcanonical work and fluctuation relations for an open system: An exactly solvable model
Abstract
We calculate the probability distribution of work for an exactly solvable model of a system interacting with its environment. The system of interest is a harmonic oscillator with a timedependent control parameter, the environment is modeled by Nindependent harmonic oscillators with arbitrary frequencies, and the systemenvironment coupling is bilinear and not necessarily weak. The initial conditions of the combined system and environment are sampled from a microcanonical distribution and the system is driven out of equilibrium by changing the control parameter according to a prescribed protocol. In the limit of infinitely large environment, i.e., N→∞, we recover the nonequilibrium work relation and Crooks's fluctuation relation. Moreover, the microcanonical Crooks relation is verified for finite environments. Finally, we show the equivalence of multitime correlation functions of the system in the infinite environment limit for canonical and microcanonical ensembles.
 Publication:

Physical Review E
 Pub Date:
 October 2013
 DOI:
 10.1103/PhysRevE.88.042136
 arXiv:
 arXiv:1311.0953
 Bibcode:
 2013PhRvE..88d2136S
 Keywords:

 05.70.Ln;
 05.20.Gg;
 05.40.Jc;
 Nonequilibrium and irreversible thermodynamics;
 Classical ensemble theory;
 Brownian motion;
 Condensed Matter  Statistical Mechanics
 EPrint:
 12 Pages