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Entropy Production in Exactly Solvable Systems.
Luca Cocconi1,2,3, Rosalba Garcia-Millan1,2,4, Zigan Zhen1,2
1Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
This study reviews entropy production, a measure of deviation from thermodynamic equilibrium. It calculates entropy production in exactly solvable systems, offering a foundation for complex non-equilibrium systems.
Area of Science:
- Statistical Mechanics
- Non-equilibrium Thermodynamics
- Stochastic Processes
Background:
- Entropy production quantifies a system's distance from thermodynamic equilibrium.
- It measures the breaking of global detailed balance and time-reversal symmetry.
- A lack of comprehensive examples hinders understanding of entropy production fundamentals.
Purpose of the Study:
- To provide a self-contained review of entropy production.
- To calculate entropy production from first principles in exactly solvable systems.
- To offer a benchmark for studying complex non-equilibrium systems.
Main Methods:
- Review of entropy production fundamentals.
- First-principles calculation of entropy production.
- Analysis of discrete- and continuous-state Markov processes.
- Examination of single- and multiple-particle systems.
Main Results:
- A catalogue of exactly solvable setups for entropy production calculation.
- Demonstration of entropy production in diverse Markov processes.
- Foundation for analyzing more complex systems like active matter.
Conclusions:
- The presented examples serve as a stepping stone for advanced studies.
- This work provides a benchmark for developing new mathematical formalisms.
- Understanding entropy production is crucial for non-equilibrium statistical mechanics.
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