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Updated: Nov 10, 2025
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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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Classical and Quantum H-Theorem Revisited: Variational Entropy and Relaxation Processes
Carlos Medel-Portugal1, Juan Manuel Solano-Altamirano2, José Luis E Carrillo-Estrada1
1Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apdo. Postal. J-48, Puebla 72570, Mexico.
Entropy (Basel, Switzerland)
|April 3, 2021
Summary
This study introduces a new framework for understanding how classical and quantum gases reach equilibrium from an out-of-equilibrium state. It extends the H-theorem to inhomogeneous systems, providing a unified approach for diverse gas types.
Area of Science:
- Statistical Mechanics
- Quantum Gases
- Thermodynamics
Background:
- Describing the approach to equilibrium for inhomogeneous classical and quantum gases is complex.
- Existing models may not fully capture the behavior of systems initially out of equilibrium.
Purpose of the Study:
- To develop a novel framework for the time-evolution of dilute classical and quantum gases towards equilibrium.
- To extend the H-theorem to spatially inhomogeneous systems.
Main Methods:
- Dividing the system into small cells and applying the local equilibrium hypothesis.
- Defining a global functional as the sum of cell H-functionals.
- Utilizing the variational method to prove the time-evolution relationship (dH/dt≤0).
Main Results:
- A unified framework is presented for classical (Maxwell-Boltzmann) and quantum (Fermi-Dirac, Bose-Einstein) gases.
- The H-functional is shown to decrease over time (dH/dt≤0), indicating a move towards equilibrium.
- The H-functionals align with the correspondence principle and can be identified with system entropy.
Conclusions:
- The proposed framework offers a generalized H-theorem for inhomogeneous systems.
- It provides insights into the relaxation processes of out-of-equilibrium gases.
- The approach unifies the description of diverse gas behaviors approaching equilibrium.
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