Responses to applied forces and the Jarzynski equality in classical oscillator systems coupled to finite baths: An exactly solvable nondissipative nonergodic model

2011/02/28 by Hideo Hasegawa
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Mathematical physics #Mathematics #Physics #Quantum Electrodynamics and Casimir Effect #Thermoelastic and Magnetoelastic Phenomena #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.84.011145

published as Phys. Rev. E 84 (2011) 0111145 · 26 pages, 6 figures, the final version with changed title accepted in Phys. Rev. E

arxiv created 2011/06/28 · openalex publication_date 2011/07/27 · arxiv updated 2015/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Responses of small open oscillator systems to applied external forces have been studied with the use of an exactly solvable classical Caldeira-Leggett model in which a harmonic oscillator (system) is coupled to finite N-body oscillators (bath) with an identical frequency (ω(n) = ω(o) for n = 1 to N). We have derived exact expressions for positions, momenta, and energy of the system in nonequilibrium states and for work performed by applied forces. A detailed study has been made on an analytical method for canonical averages of physical quantities over the initial equilibrium state, which is much superior to numerical averages commonly adopted in simulations of small systems. The calculated energy of the system which is strongly coupled to a finite bath is fluctuating but nondissipative. It has been shown that the Jarzynski equality is valid in nondissipative nonergodic open oscillator systems regardless of the rate of applied ramp force.

Citations

• Work Fluctuation Theorems for Harmonic Oscillators
• A note on the Jarzynski equality
• The Jarzynski relation, fluctuation theorems, and stochastic thermodynamics for non-Markovian processes
• Quantum tunnelling in a dissipative system
• A fluctuation theorem for non-equilibrium relaxational systems driven by external forces
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• Reexamination of experimental tests of the fluctuation theorem
• Practical Applicability of the Jarzynski Relation in Statistical Mechanics: A Pedagogical Example
• The Nonequilibrium Thermodynamics of Small Systems
• Fluctuation theorems for harmonic oscillators