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Updated: Jun 22, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Entropy of continuous Markov processes in local thermal equilibrium
1Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata and Instituto de Investigaciones Físicas de Mar del Plata (Consejo Nacional de Investigaciones Científicas y Técnicas), 7600 Mar del Plata, Argentina.
Summary
This study analyzes Boltzmann
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Physical Chemistry
Background:
- Analysis of Boltzmann's entropy for continuous Markov processes in local thermal equilibrium.
- Consideration of systems in contact with a reservoir at temperature T.
Purpose of the Study:
- Derive an equation for entropy density from the Fokker-Planck equation with constant coefficients and detailed balance.
- Obtain expressions for transport coefficients and entropy production terms.
- Analyze the multicomponent case and derive Prigogine's theorem.
Main Methods:
- Mathematical derivation based on Fokker-Planck equation.
- Analysis of continuous Markov processes.
- Application of detailed balance condition.
Main Results:
- An equation for entropy density was derived.
- Expressions for transport coefficients as functions of the diffusion matrix were obtained.
- Entropy production terms for the system and system-reservoir were calculated.
- Prigogine's theorem of minimum entropy production was derived for reaction diffusion systems.
Conclusions:
- The derivations provide a framework for understanding nonequilibrium diffusion systems.
- Established relations among transport coefficients were reproduced.
- The study offers insights into the behavior of systems far from equilibrium.
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