Maximum speed of dissipation

Abstract

We derive statistical-mechanical speed limits on dissipation from the classical, chaotic dynamics of many-particle systems. In one, the rate of irreversible entropy production in the environment is the maximum speed of a deterministic system out of equilibrium, ${\bar{S}}_e/k_B\ge 1/2\Delta t$, and its inverse is the minimum time to execute the process, $\Delta t\ge k_B/2{\bar{S}}_e$. Starting with deterministic fluctuation theorems, we show there is a corresponding class of speed limits for physical observables measuring dissipation rates. For example, in many-particle systems interacting with a deterministic thermostat, there is a trade-off between the time to evolve between states and the heat flux, $\bar{Q}\Delta t\ge k_{B}T/2$. These bounds constrain the relationship between dissipation and time during nonstationary process, including transient excursions from steady states.

arXiv commentnew plots added, some edits in the text

References in corpus (26)

• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• The maximum speed of dynamical evolution
• The Nonequilibrium Thermodynamics of Small Systems
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Quantum limits to dynamical evolution
• Speed Limit for Classical Stochastic Processes
• Quantum Speed Limits Across the Quantum-to-Classical Transition
• Quantum Speed Limit is Not Quantum
• Uncertainty relations in stochastic processes: An information inequality approach
• Probing rare physical trajectories with Lyapunov weighted dynamics
• Time-information uncertainty relations in thermodynamics
• Improved bounds on entropy production in living systems
• Stochastic time-evolution, information geometry and the Cramer-Rao Bound
• The dissipation-time uncertainty relation
• Note on Two Theorems in Nonequilibrium Statistical Mechanics
• Lyapunov Exponents and KS Entropy for the Lorentz Gas at Low Densities
• Nonequilibrium uncertainty principle from information geometry
• Critical fluctuations and slowing down of chaos
• Ergodicity of a Singly-Thermostated Harmonic Oscillator
• Diverging quantum speed limits: a herald of classicality
• Energy Dissipation Bounds for Autonomous Thermodynamic Cycles
• Thermostatting by deterministic scattering
• The Equivalence of Dissipation from Gibbs' Entropy Production with Phase-Volume Loss in Ergodic Heat-Conducting Oscillators
• Self-averaging fluctuations in the chaoticity of simple fluids
• What does dynamical systems theory teach us about fluids?
• Density matrix formulation of dynamical systems

Cited by in corpus (2)

• Spectral bounds on the entropy flow rate and Lyapunov exponents in differentiable dynamical systems
• Phase space contraction rate for classical mixed states