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Overdamped stochastic thermodynamics with multiple reservoirs
Yûto Murashita1, Massimiliano Esposito2
1Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan.
Physical Review. E
|January 14, 2017
Summary
We developed a new theory for stochastic thermodynamics in overdamped systems with multiple heat reservoirs, revealing differences from naive theories. This work clarifies heat conduction in complex systems.
Area of Science:
- Statistical Mechanics
- Non-equilibrium Thermodynamics
- Soft Matter Physics
Background:
- Stochastic thermodynamics describes heat, work, and entropy in small systems.
- Existing theories often simplify systems to single reservoirs or overdamped dynamics.
- The behavior of systems with multiple reservoirs and underdamped dynamics is less understood.
Purpose of the Study:
- To derive the overdamped limit of stochastic thermodynamics for systems with multiple reservoirs.
- To compare this derived theory with naive approaches based on overdamped Langevin or Fokker-Planck equations.
- To investigate the fundamental fluctuation theorems and heat statistics in these systems.
Main Methods:
- Established stochastic thermodynamics for underdamped Langevin systems coupled to multiple reservoirs.
- Employed timescale separation techniques to derive the corresponding overdamped limit.
- Analyzed heat statistics for a Brownian particle on a ring with two reservoirs and a nonconservative force.
Main Results:
- The derived overdamped theory differs from naive theories, especially with multiple reservoirs.
- This discrepancy arises because fast momentum dynamics reach a non-equilibrium state, enabling heat conduction.
- Both underdamped and overdamped theories satisfy fundamental fluctuation theorems.
Conclusions:
- The study provides a more accurate stochastic thermodynamic framework for overdamped systems with multiple reservoirs.
- The findings highlight the importance of considering non-equilibrium momentum dynamics in coarse-grained descriptions.
- Analytical predictions for heat statistics in a model system confirm the validity of the derived theories.
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