Classical Canonical Distribution for Dissipative Systems

Abstract

In this paper we derive the canonical distribution as a stationary solution of the Liouville equation for the classical dissipative system. Dissipative classical systems can have stationary states look like canonical Gibbs distributions. The condition for non-potential forces which leads to this stationary solution is very simple: the power of the non-potential forces must be directly proportional to the velocity of the Gibbs phase (phase entropy density) change. The example of the canonical distribution for a linear oscillator with friction is considered.

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References in corpus (4)

• Quantization of non-Hamiltonian and Dissipative Systems
• Quantum Computer with Mixed States and Four-Valued Logic
• Pure Stationary States of Open Quantum Systems
• Stationary States of Dissipative Quantum Systems

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• Nonholonomic Constraints with Fractional Derivatives
• Multipole Moments of Fractal Distribution of Charges
• Transport Equations from Liouville Equations for Fractional Systems
• Fokker-Planck Equation for Fractional Systems
• Path Integral for Quantum Operations
• Stationary Solutions of Liouville Equations for Non-Hamiltonian Systems
• Thermodynamics of Few-Particle Systems