Practical Applicability of the Jarzynski Relation in Statistical Mechanics: A Pedagogical Example

2005/01/27 by Rhonald C. Lua, R. C. Lua, Alexander Y. Grosberg +1 · 6 citations
Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Field-Flow Fractionation Techniques #Quantum Electrodynamics and Casimir Effect #cond-mat.stat-mech

paper · pdf · doi:10.1021/jp0455428

published as J. Phys. Chem. B. ; (Article); 2005; 109(14); 6805-6811. · 15 pages, 7 figures, submitted to JPC

openalex publication_date 2005/01/27 · arxiv created 2005/02/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We suggest and discuss a simple model of an ideal gas under the piston to gain an insight into the workings of the Jarzynski identity connecting the average exponential of the work over the nonequilibrium trajectories with the equilibrium free energy. We show that the identity is valid for our system, due to the very rapid molecules belonging to the tail of the Maxwell distribution. For the most interesting extreme, when the system volume is large, while the piston is moving with great speed (compared to thermal velocity) for a very short time, the necessary number of independent experimental runs to obtain a reasonable approximation for the free energy from averaging the nonequilibrium work grows exponentially with the system size.

Citations

• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach

Cited by

• A nonequilibrium distribution for stochastic thermodynamics
• Work distribution for the adiabatic compression of a dilute and interacting classical gas
• Stochastic resonance and heat fluctuations in a driven double-well system
• Nonequilibrium fluctuation theorems in the presence of local heating
• On the efficiency of path sampling methods for the calculation of free energies from non-equilibrium simulations
• Phase transition in the Jarzynski estimator of free energy differences

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