Validation of the Jarzynski relation for a system with strong thermal coupling: an isothermal ideal gas model

Abstract

We revisit the paradigm of an ideal gas under isothermal conditions. A moving piston performs work on an ideal gas in a container that is strongly coupled to a heat reservoir. The thermal coupling is modelled by stochastic scattering at the boundaries. In contrast to recent studies of an adiabatic ideal gas with a piston [R.C. Lua and A.Y. Grosberg, \textit{J. Phys. Chem. B} 109, 6805 (2005); I. Bena et al., \textit{Europhys. Lett.} 71, 879 (2005)], container and piston stay in contact with the heat bath during the work process. Under this condition the heat reservoir as well as the system depend on the work parameter $\lambda$ and microscopic reversibility is broken for a moving piston. Our model is thus not included in the class of systems for which the non-equilibrium work theorem has been derived rigorously either by Hamiltonian [C. Jarzynski, \textit{J. Stat. Mech.} P09005 (2004)] or stochastic methods [G.E. Crooks, \textit{J. Stat. Phys.} 90, 1481 (1998)]. Nevertheless the validity of the non-equilibrium work theorem is confirmed both numerically for a wide range of parameter values and analytically in the limit of a very fast moving piston, i.e. in the far non-equilibrium regime.

11 pages, 8 figures

References in corpus (6)

• A nonequilibrium equality for free energy differences
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Rare events and the convergence of exponentially averaged work values
• On practical applicability of the Jarzynski relation in statistical mechanics: a pedagogical example
• Rules for transition rates in nonequilibrium steady states
• Jarzynski equality for the Jepsen gas

Cited by in corpus (6)

• Efficiency of Single Particle Engines
• Carnot process with a single particle
• Stochastic Thermodynamics of a Particle in a Box
• Statistical work-energy theorems in deterministic dynamics
• Non-equilibrium dynamics of the piston in the Szilard engine
• Thermodynamics of slow solutions to the Gas-Piston equations