Coarse-graining nonequilibrium diffusions with Markov chains

Abstract

We investigate nonequilibrium steady-state dynamics in both continuous- and discrete-state stochastic processes. Our analysis focuses on planar diffusion dynamics and their coarse-grained approximations by discrete-state Markov chains. Using finite-volume approximations, we derive an approximate master equation directly from the underlying diffusion and show that this discretisation preserves key features of the nonequilibrium steady-state. In particular, we show that the entropy production rate of the approximation converges as the number of discrete states goes to the limit. These results are illustrated with analytically solvable diffusions and numerical experiments on nonlinear processes, demonstrating how this approach can be used to explore the dependence of the entropy production rate on model parameters. Finally, we address the problem of inferring discrete-state Markov models from continuous stochastic trajectories. We show that discrete-state models significantly underestimate the true entropy production rate. However, we also show that they can provide tests to determine if a stationary planar diffusion is out of equilibrium. This property is illustrated with both simulated data and empirical trajectories from schooling fish.

26 pages, 21 figures

References in corpus (34)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Statistical mechanics for natural flocks of birds
• Random walks and diffusion on networks
• Macroscopic fluctuation theory
• How far from equilibrium is active matter?
• Non-reciprocal phase transitions
• Memory in network flows and its effects on spreading dynamics and community detection
• Stochastic thermodynamics under coarse-graining
• Nonequilibrium Physics in Biology
• Quantifying dissipation using fluctuating currents
• Kuramoto model of synchronization: Equilibrium and nonequilibrium aspects
• Noise-Induced Schooling of Fish
• Inferring broken detailed balance in the absence of observable currents
• On the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusion
• Local equilibrium in bird flocks
• Inferring the dynamics of underdamped stochastic systems
• Coarse-Grained Modelling Out of Equilibrium
• Learning force fields from stochastic trajectories
• Structure preserving schemes for nonlinear Fokker-Planck equations and applications
• Large deviation approach to nonequilibrium systems
• A generalization of Onsager's reciprocity relations to gradient flows with nonlinear mobility
• A Thermodynamically consistent model of the post-translational Kai circadian clock
• Physically consistent numerical solver for time-dependent Fokker-Planck equations
• Canonical structure and orthogonality of forces and currents in irreversible Markov chains
• Characterising the nonequilibrium stationary states of Ornstein-Uhlenbeck processes
• Entropy production for coarse-grained dynamics
• Local detailed balance across scales: from diffusions to jump processes and beyond
• The Scharfetter--Gummel scheme for aggregation-diffusion equations
• Broken detailed balance and entropy production in directed networks
• On the waiting time distribution for continuous stochastic systems
• Nonequilibrium limit cycle oscillators: fluctuations in hair bundle dynamics
• Nonequilibrium physics of brain dynamics
• State aggregations in Markov chains and block models of networks
• Entropy production from waiting-time distributions for overdamped Langevin dynamics