Convergence to Gibbs equilibrium - unveiling the mystery

Abstract

We consider general hamiltonian systems with quadratic interaction potential and $N<\infty$ degrees of freedom, only $m$ of which have contact with external world, that is subjected to damping and random stationary external forces. We show that, as $t\to \infty$, already for $m=1$, the unique limiting distribution exists for almost all interactions. Moreover, it is Gibbs if the external force is the white noise, but typically not Gibbs for gaussian processes with smooth trajectories. This conclusion survives also in the thermodynamic limit $N\to \infty$.

References in corpus (2)

• Harmonic Chain with Weak Dissipation
• Linear Hamiltonian Systems under Microscopic Random Influence

Cited by in corpus (4)

• Liouville ergodicity of linear multi-particle hamiltonian system with one marked particle velocity flips
• Convergence to equilibrium for many particle systems
• Convergence to equilibrium due to collisions with external particles
• Uniformly Bounded Initial Chaos in Large System Often Intensifies Infinitely