Jarzynski equation for a simple quantum system: Comparing two definitions of workA. Engel and R. Nolte
Institut für Physik, Carl-von-Ossietzky-Universität - 26111 Oldenburg, Germany
received 20 December 2006; accepted in final form 21 May 2007; published July 2007
published online 6 June 2007
The validity of the Jarzynski equation for a very simple, exactly solvable quantum system is analyzed. The implications of two different definitions of work proposed in the literature are investigated. The first one derives from measurements of the system energy at the beginning and at the end of the process under consideration making the work a classical stochastic variable with transition probabilities derived from quantum-mechanics. In the second definition an operator of work is introduced and the average in the Jarzynski equation is a quantum expectation value. For the first definition a general quantum-mechanical version of the Jarzynski equation is known to hold. For the second one the Jarzynski equation fails to yield the free energy difference at low temperature.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
05.30.-d - Quantum statistical mechanics.
05.70.Ln - Nonequilibrium and irreversible thermodynamics.
© Europhysics Letters Association 2007