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Three faces of the second law. I. Master equation formulation
Massimiliano Esposito1, Christian Van den Broeck
1Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
We developed a new framework for stochastic thermodynamics under nonequilibrium conditions and time-dependent forces. This approach reveals a split in the second law, yielding three new relations for these complex systems.
Area of Science:
- Physics
- Physical Chemistry
- Statistical Mechanics
Background:
- Stochastic thermodynamics typically assumes systems are at or near equilibrium.
- Nonequilibrium constraints and time-dependent driving forces complicate thermodynamic descriptions.
- Existing models struggle to accurately capture energy flow and entropy production in driven, non-equilibrium systems.
Purpose of the Study:
- To formulate stochastic thermodynamics for systems under nonequilibrium constraints and time-dependent external forces.
- To investigate the implications of broken detailed balance at steady state for thermodynamic laws.
- To develop a theoretical framework applicable to complex, driven systems far from equilibrium.
Main Methods:
- Utilizing a master equation based approach.
- Developing a theoretical formulation for stochastic thermodynamics.
- Analyzing systems subjected to nonequilibrium constraints and time-dependent driving forces.
Main Results:
- A splitting of the second law of thermodynamics was identified under the studied conditions.
- Three novel second-law-like relations were derived.
- The general results were demonstrated and validated using specific, solvable models.
Conclusions:
- The proposed formulation provides a robust framework for stochastic thermodynamics in driven, non-equilibrium systems.
- The derived relations offer new insights into energy and entropy dynamics beyond equilibrium assumptions.
- This work extends the applicability of thermodynamic principles to a broader range of complex physical and chemical systems.
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