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Onsager coefficients for systems with periodic potentials.

Alexandre Rosas1, Christian Van den Broeck2, Katja Lindenberg3

  • 1Departamento de Física, CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, 58059-900 João Pessoa, Brazil.

Physical Review. E
|December 15, 2016
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Summary
This summary is machine-generated.

We analyze a Markovian stochastic engine using periodic modulation. This study derives Onsager coefficients for work transfer and validates results with a kangaroo process, showing excellent agreement with simulations.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Stochastic Processes

Background:

  • Stochastic engines are crucial for understanding energy conversion in systems driven by random fluctuations.
  • Periodic modulation is a common method to control and analyze the behavior of these engines.
  • Linear response theory provides a framework to study system behavior under small perturbations.

Purpose of the Study:

  • To perform a thermodynamic analysis of a Markovian stochastic engine driven by spatial and temporal periodic modulation.
  • To derive analytic expressions for Onsager coefficients in the linear response regime for work transfer.
  • To investigate the entropy production, power, and efficiency of a specific model, the kangaroo process.

Main Methods:

  • Thermodynamic analysis of a d-dimensional Markovian stochastic engine.
  • Derivation of analytic expressions for Onsager coefficients.
  • Modeling a kangaroo process coupling orthogonal directions.
  • Numerical simulations for validation.

Main Results:

  • Analytic expressions for Onsager coefficients characterizing linear response work transfer were derived.
  • Explicit results for a Markovian kangaroo process were obtained.
  • Excellent agreement was found between derived expressions and numerical simulations.
  • Expressions for entropy production, power, and efficiency of the kangaroo process were derived and discussed.

Conclusions:

  • The study provides a theoretical framework for analyzing Markovian stochastic engines under periodic modulation.
  • The derived Onsager coefficients accurately describe work transfer in the linear response regime.
  • The kangaroo process serves as a valid and illustrative example, confirming the theoretical predictions.