Thermalization of a Brownian particle via coupling to low-dimensional chaos

Abstract

It is shown that a paradigm of classical statistical mechanics --- the thermalization of a Brownian particle --- has a low-dimensional, deterministic analogue: when a heavy, slow system is coupled to fast deterministic chaos, the resultant forces drive the slow degrees of freedom toward a state of statistical equilibrium with the fast degrees. This illustrates how concepts useful in statistical mechanics may apply in situations where low-dimensional chaos exists.

Revtex, 11 pages, no figures.

Cited by in corpus (38)

• Quantum dissipation due to the interaction with chaotic degrees-of-freedom and the correspondence principle
• Chaos and energy spreading for time-Dependent Hamiltonians, and the various Regimes in the theory of Quantum Dissipation
• A Dynamic Approach to the Thermodynamics of Superdiffusion
• Quantum-Mechanical Non-Perturbative Response of Driven Chaotic Mesoscopic Systems
• Quantum Dissipation versus Classical Dissipation for Generalized Brownian Motion
• Finite Bath Fluctuation Theorem
• Minimal Fokker-Planck theory for the thermalization of mesoscopic subsystems
• Regimes of heating and dynamical response in driven many-body localized systems
• From Langevin to generalized Langevin equations for the nonequilibrium Rouse model
• The Levy diffusion as an effect of sporadic randomness
• Ideal quantum gas in expanding cavity: nature of non-adiabatic force
• Chaoticity in Vibrating Nuclear Billiards
• One-body dissipation and chaotic dynamics in a classical simulation of a nuclear gas
• Classical Dissipation and Asymptotic Equilibrium via Interaction with Chaotic Systems
• Least Rattling Feedback from Strong Time-scale Separation
• Energy Dissipation Via Coupling With a Finite Chaotic Environment
• Emergent Newtonian dynamics and the geometric origin of mass
• Dephasing due to the interaction with chaotic degrees of freedom
• Quantal Brownian Motion - Dephasing and Dissipation
• Rate of energy absorption by a closed ballistic ring
• Correlations in the Adiabatic Response of Chaotic Systems
• Thermodynamic selection: mechanisms and scenarios
• Quantum Dissipation and Decoherence via Interaction with Low-Dimensional Chaos: a Feynman-Vernon Approach
• Stochastic Models of Exotic Transport
• Quantum response of weakly chaotic systems
• Free energy for non-equilibrium quasi-stationary states
• "Weak Quantum Chaos" and its resistor network modeling
• Energy absorption by "sparse" systems: beyond linear response theory
• The Quantum-Classical Crossover in the Adiabatic Response of Chaotic Systems
• Relationship between nonlinearities and thermalization in classical open systems: The role of the interaction range
• Relating the thermodynamic arrow of time to the causal arrow
• Arrows of Time and Chaotic Properties of the Cosmic Background Radiation
• Non-extensive thermodynamics and stationary processes of localization
• Geometric magnetism in classical transport theory
• Verification of finite bath fluctuation theorem for a non-ergodic system
• Quantum anomalies and linear response theory
• Representation of intermediate time-scale motions in stochastic modeling: Analysis on stochastic description of classical Hamiltonian dynamics in relation with measurement imperfection
• Direct Quantization of Open Dissipative Systems