Classical Dissipation and Asymptotic Equilibrium via Interaction with Chaotic Systems

Abstract

We study the energy flow between a one dimensional oscillator and a chaotic system with two degrees of freedom in the weak coupling limit. The oscillator's observables are averaged over an initially microcanonical ensemble of trajectories of the chaotic system, which plays the role of an environment for the oscillator. We show numerically that the oscillator's average energy exhibits irreversible dynamics and `thermal' equilibrium at long times. We use linear response theory to describe the dynamics at short times and we derive a condition for the absorption or dissipation of energy by the oscillator from the chaotic system. The equilibrium properties at long times, including the average equilibrium energies and the energy distributions, are explained with the help of statistical arguments. We also check that the concept of temperature defined in terms of the `volume entropy' agrees very well with these energy istributions.

arXiv commentrevised text, new references, 36 pages, 9 figures

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Cited by in corpus (8)

• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Chaotic motion at the emergence of the time averaged energy decay
• Exponential energy growth in adiabatically changing Hamiltonian Systems
• Energy Dissipation Via Coupling With a Finite Chaotic Environment
• Quantum Dissipation and Decoherence via Interaction with Low-Dimensional Chaos: a Feynman-Vernon Approach
• Energy transfer dynamics and thermalization of two oscillators interacting via chaos
• Relationship between nonlinearities and thermalization in classical open systems: The role of the interaction range
• Verification of finite bath fluctuation theorem for a non-ergodic system