Heat leakage in overdamped harmonic systems

Abstract

We investigate the occurrence of heat leakages in overdamped Brownian harmonic systems. We exactly compute the underdamped and overdamped stochastic heats exchanged with the bath for a sudden frequency or temperature switch. We show that the underdamped heat reduces to the corresponding overdamped expression in the limit of large friction for the isothermal process. However, we establish that this is not the case for the isochoric transformation. We microscopically derive the additionally generated heat leakage and relate its origin to the initial relaxation of the velocity of the system. Our results highlight the limitations of the overdamped approximation for the evaluation of the stochastic heat in systems with changing bath temperature.

arXiv comment5 pages, 4 figures

References in corpus (16)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Efficiency at maximum power: An analytically solvable model for stochastic heat engines
• Efficiency at maximum power of low dissipation Carnot engines
• Brownian Carnot engine
• Universality of efficiency at maximum power
• An all-optical nanomechanical heat engine
• Anomalous thermodynamics at the micro-scale
• Adiabatic processes realized with a trapped Brownian particle
• Inattainability of Carnot efficiency in the Brownian heat engine
• Rectification of Fluctuations in an Underdamped Ratchet
• Optimal performance of periodically driven, stochastic heat engines under limited control
• The Carnot Cycle for Small Systems: Irreversibility and the Cost of Operations
• Inertial effects in B{ü}ttiker-Landauer Motor and Refrigerator at the Overdamped Limit
• Underdamped stochastic heat engine at maximum efficiency
• Measuring kinetic energy changes in the mesoscale with low acquisition rates

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