Microcanonical ensemble out of equilibrium

Abstract

Introduced by Boltzmann under the name "monode," the microcanonical ensemble serves as the fundamental representation of equilibrium thermodynamics in statistical mechanics by counting all possible realizations of a system's states. Ensemble theory connects this idea with probability and information theory, leading to the notion of Shannon-Gibbs entropy and, ultimately, to the principle of maximum caliber describing trajectories of systems--in and out of equilibrium. While the latter phenomenological generalization reproduces many results of nonequilibrium thermodynamics, given a proper choice of observables, its physical justification remains an open area of research. What is the microscopic origin and physical interpretation of this variational approach? What guides the choice of relevant observables? We address these questions by extending Boltzmann's method to a microcanonical caliber principle and counting realizations of a system's trajectories--all assumed equally probable. Maximizing the microcanonical caliber under the imposed constraints, we systematically develop generalized detailed-balance relations, clarify the statistical origins of inhomogeneous transport, and provide an independent derivation of key equations from stochastic thermodynamics. This approach introduces a dynamical ensemble theory for nonequilibrium steady states in spatially extended and active systems. While verifying the equivalence of ensembles, e.g. those of Norton and Thevenin, our framework contests other common assumptions about nonequilibrium regimes, with supporting evidence provided by stochastic simulations. Our theory suggests further connections to the first principles of microscopic dynamics in classical statistical mechanics, which are essential for investigating systems where the necessary conditions for thermodynamic behavior are not satisfied.

21 pages, 3 figures

References in corpus (55)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Active Particles in Complex and Crowded Environments
• The large deviation approach to statistical mechanics
• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states
• Stochastic thermodynamics under coarse-graining
• Thermodynamic formalism for systems with Markov dynamics
• Nonequilibrium Markov processes conditioned on large deviations
• Physics of Active Emulsions
• Towards a 'Thermodynamics' of Active Matter
• A review of linear response theory for general differentiable dynamical systems
• Nonequilibrium microcanonical and canonical ensembles and their equivalence
• Localization of maximal entropy random walk
• The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
• Introduction to dynamical large deviations of Markov processes
• Frenesy: time-symmetric dynamical activity in nonequilibria
• Local detailed balance
• Rules for transition rates in nonequilibrium steady states
• Entropy production and coarse-graining in Markov processes
• Thermodynamics and its Prediction and CALPHAD Modeling: Review, State of the Art, and Perspectives
• Collective power: Minimal model for thermodynamics of nonequilibrium phase transitions
• Stochastic Thermodynamics of Non-Linear Electronic Circuits: A Realistic Framework for Computing around kT
• Detailed balance has a counterpart in non-equilibrium steady states
• Teaching the Principles of Statistical Dynamics
• Molecular Dynamics in a Grand Ensemble: Bergmann-Lebowitz model and Adaptive Resolution Simulation
• Large-deviation principles, stochastic effective actions, path entropies, and the structure and meaning of thermodynamic descriptions
• Thermodynamics of active field theories: Energetic cost of coupling to reservoirs
• Markov processes follow from the principle of Maximum Caliber
• Non-equilibrium steady states : maximization of the Shannon entropy associated to the distribution of dynamical trajectories in the presence of constraints
• Fluctuation preserving coarse graining for biochemical systems
• Macroscopic Stochastic Thermodynamics
• Topology protects chiral edge currents in stochastic systems
• Effects of breaking vibrational energy equipartition on measurements of temperature in macroscopic oscillators subject to heat flux
• A mechanical model for Fourier's law of heat conduction
• A derivation of the master equation from path entropy maximization
• On the relaxation to nonequilibrium steady states
• Nonequilibrium steady states in contact: Approximate thermodynamic structure and zero-th law for driven lattice gases
• Maximum caliber is a general variational principle for nonequilibrium statistical mechanics
• Active matter, microreversibility, and thermodynamics
• How Electronic Dynamics with Pauli Exclusion Produces Fermi-Dirac Statistics
• Fourier's law based on microscopic dynamics
• Nonequilibrium Thermodynamics of Non-Ideal Reaction-Diffusion Systems: Implications for Active Self-Organization
• Enhanced diffusion of a tracer particle in a lattice model of a crowded active system
• A topological mechanism for robust and efficient global oscillations in biological networks
• Stationary properties of maximum entropy random walks
• Poissonian cellular Potts models reveal nonequilibrium kinetics of cell sorting
• Random walk on the simple symmetric exclusion process
• Microcanonical Origin of the Maximum Entropy Principle for Open Systems
• Pushing run-and-tumble particles through a rugged channel
• Quantifying configurational information for a stochastic particle in a flow-field
• Towards a liquid-state theory for active matter
• Non-Equilibrium Statistical Physics Beyond the Ideal Heat Bath Approximation
• Non Equilibrium Transitions in a Polymer Replication Ensemble
• Effective Affinity for Generic Currents in Markov Processes
• Repulsive particle interactions enable selective information processing at cellular interfaces