Spectral bounds on the entropy flow rate and Lyapunov exponents in differentiable dynamical systems
arXiv:2501.04485 · doi:10.1088/1751-8121/ad8f06
Abstract
Some microscopic dynamics are also macroscopically irreversible, dissipating energy and producing entropy. For many-particle systems interacting with deterministic thermostats, the rate of thermodynamic entropy dissipated to the environment is the average rate at which phase space contracts. Here, we use this identity and the properties of a classical density matrix to derive upper and lower bounds on the entropy flow rate with the spectral properties of the local stability matrix. These bounds are an extension of more fundamental bounds on the Lyapunov exponents and phase space contraction rate of continuous-time dynamical systems. They are maximal and minimal rates of entropy production, heat transfer, and transport coefficients set by the underlying dynamics of the system and deterministic thermostat. Because these limits on the macroscopic dissipation derive from the density matrix and the local stability matrix, they are numerically computable from the molecular dynamics. As an illustration, we show that these bounds are on the electrical conductivity for a system of charged particles subject to an electric field.
arXiv commentPublished in J. Phys. A: Math. Theor., unnecessary autolinking in the abstract removed
References in corpus (21)
- Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics
- Geometric approach to Hamiltonian dynamics and statistical mechanics
- Frontiers of chaotic advection
- Chaotic Scattering Theory, Thermodynamic Formalism, and Transport Coefficients
- Chaotic Scattering Theory of Transport and Reaction-Rate Coefficients
- Hamiltonian dynamics, nanosystems, and nonequilibrium statistical mechanics
- On the geometry of Hamiltonian chaos
- Note on Phase Space Contraction and Entropy Production in Thermostatted Hamiltonian Systems
- Lyapunov instabilities of Lennard-Jones fluids
- Entropy Production : From Open Volume Preserving to Dissipative Systems
- Many-body Chaos in Thermalised Fluids
- Characterizing Weak Chaos using Time Series of Lyapunov Exponents
- Critical fluctuations and slowing down of chaos
- Ergodicity of a Singly-Thermostated Harmonic Oscillator
- Thermostatting by deterministic scattering
- Jacobian deformation ellipsoid and Lyapunov stability analysis revisited
- 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
- Density matrix formulation of dynamical systems
- On thermostats and entropy production
- Maximum speed of dissipation