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Updated: Apr 12, 2026
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
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Stochastic approach to equilibrium and nonequilibrium thermodynamics
Tânia Tomé1, Mário J de Oliveira1
1Instituto de Física, Universidade de São Paulo, Caixa Postal 66318 05314-970 São Paulo, São Paulo, Brazil.
Summary
We present a stochastic thermodynamics approach using master and Fokker-Planck equations. This framework explains macroscopic thermodynamic laws from microscopic dynamics, including entropy production and nonequilibrium steady states.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Physical Chemistry
Background:
- Thermodynamics traditionally describes macroscopic systems.
- Stochastic dynamics offers a microscopic perspective on thermodynamic processes.
- Bridging these scales requires a robust theoretical framework.
Purpose of the Study:
- To develop a stochastic approach to thermodynamics.
- To establish fundamental assumptions for entropy and entropy production.
- To derive macroscopic laws from stochastic dynamics.
Main Methods:
- Utilizing discrete (master equation) and continuous (Fokker-Planck) stochastic dynamics.
- Defining entropy and entropy production rate based on non-negativity and equilibrium conditions.
- Analyzing interacting systems with multiple degrees of freedom.
Main Results:
- Derived macroscopic laws from stochastic dynamics for equilibrium and nonequilibrium systems.
- Investigated quasiequilibrium processes and equilibrium surface convexity.
- Characterized monotonic behavior of thermodynamic potentials and entropy.
- Established the bilinear form of entropy production rate, Onsager coefficients, and reciprocal relations.
- Studied nonequilibrium steady states in chemical reactions.
Conclusions:
- The stochastic approach provides a unified framework for thermodynamics.
- Macroscopic laws emerge naturally from underlying stochastic dynamics.
- The framework is applicable to diverse systems, including those far from equilibrium.
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