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Boltzmann's H theorem for systems with frictional dissipation
1Associação Euratom-IST, Instituto de Plasmas e Fusão Nuclear-Laboratório Associado, Instituto Superior Técnico, 1049-001 Lisboa, Portugal. bizarro@ipfn.ist.utl.pt
Summary
This study refines Boltzmann
Area of Science:
- Statistical Mechanics
- Non-equilibrium Thermodynamics
Background:
- Boltzmann's H theorem describes entropy in isolated systems.
- Frictional forces and fluctuations are crucial in open systems.
Purpose of the Study:
- To refine Boltzmann's H theorem for systems with friction and fluctuations.
- To investigate the behavior of entropy in non-equilibrium systems.
Main Methods:
- Utilizing Boltzmann's equation with added Fokker-Planck term for fluctuations.
- Analyzing systems under viscous drag (friction coefficient γ).
Main Results:
- Modified H theorem: dH/dt ≤ γ, bounding the rate of entropy increase.
- The classical H theorem is updated to account for frictional dissipation.
- An alternative Clausius inequality form is derived for systems near thermal equilibrium.
Conclusions:
- The refined H theorem provides a more accurate description of entropy in dissipative systems.
- Frictional dissipation fundamentally limits the rate of entropy increase.
- The study offers insights into non-equilibrium statistical mechanics and thermodynamics.
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