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Entropy production in a non-Markovian environment
Aki Kutvonen1, Tapio Ala-Nissila1,2, Jukka Pekola3
1COMP Center of Excellence, Department of Applied Physics, Aalto University School of Science, P.O. Box 11000, FI-00076 Aalto, Espoo, Finland.
Summary
This study introduces a non-Markovian model for open systems, revealing new entropy production terms crucial for understanding fluctuation relations in driven systems. These findings extend thermodynamics to small, non-equilibrium scales.
Area of Science:
- Physics
- Non-equilibrium Thermodynamics
- Statistical Mechanics
Background:
- Stochastic thermodynamics and fluctuation relations extend classical thermodynamics to small, non-equilibrium systems.
- Current models often assume Markovian dynamics, which may not hold for driven systems.
- The validity of the Markovian approximation in non-equilibrium conditions is questionable.
Purpose of the Study:
- To introduce an explicitly non-Markovian model for open system dynamics.
- To investigate the impact of system-environment correlations on thermodynamic variables.
- To derive modified fluctuation relations for entropy in non-equilibrium systems.
Main Methods:
- Development of a non-Markovian model for open systems.
- Analysis of correlations between system and environment.
- Derivation of non-Markovian entropy production terms.
- Explicit derivation of modified fluctuation relations for an overheated single electron box.
Main Results:
- Introduced a novel non-Markovian dynamics model for open systems.
- Identified a new non-Markovian entropy production term arising from system-environment correlations.
- Demonstrated that non-Markovian components are essential for recovering fluctuation relations.
- Derived modified fluctuation relations for an overheated single electron box.
Conclusions:
- The Markovian approximation is insufficient for driven non-equilibrium systems.
- Non-Markovian dynamics and associated entropy production terms are critical for accurate thermodynamic descriptions.
- Modified fluctuation relations are necessary to account for non-Markovian effects in small systems.
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