Cycle representatives for the coarse-graining of systems driven into a non-equilibrium steady state

Abstract

A major current challenge poses the systematic construction of coarse-grained models that are dynamically consistent, and, moreover, might be used for systems driven out of thermal equilibrium. Here we present a novel prescription that extends the Markov state modelling approach to driven systems. The first step is to construct a complex network of microstates from detailed atomistic simulations with transition rates that break detailed balance. The coarse-graining is then carried out in the cycle space of this network. To this end we introduce the concept of representatives, which stand for many cycles with similar properties. We show how to find these cycle communities using well-developed standard algorithms. Removing all cycles except for the representatives defines the coarse-grained model, which is mapped back onto a network with far fewer states and renormalized transition rates that, however, preserve the entropy production of the original network. Our approach is illustrated and validated for a single driven particle.

References in corpus (9)

• Fast unfolding of communities in large networks
• Thermodynamic uncertainty relation for biomolecular processes
• Optimal finite-time processes in stochastic thermodynamics
• Fluctuation relations and coarse-graining
• Entropy production and coarse-graining in Markov processes
• Role of External Flow and Frame Invariance in Stochastic Thermodynamics
• Effective rates from thermodynamically consistent coarse-graining of models for molecular motors with probe particles
• Stochastic thermodynamics of fluctuating density fields: Non-equilibrium free energy differences under coarse-graining
• Cycle/cocycle oblique projections on oriented graphs

Cited by in corpus (18)

• VAMPnets: Deep learning of molecular kinetics
• Coarse-Grained Modelling Out of Equilibrium
• Special Topic: Markov Models of Molecular Kinetics
• Thermodynamically Consistent Coarse Graining of Biocatalysts beyond Michaelis--Menten
• Active Brownian particles driven by constant affinity
• Violation of Local Detailed Balance Despite a Clear Time-Scale Separation
• Optimal data-driven estimation of generalized Markov state models for non-equilibrium dynamics
• Fluctuations of Apparent Entropy Production in Networks with Hidden Slow Degrees of Freedom
• Effective thermodynamics of two interacting underdamped Brownian particles
• Relation between topology and heat currents in multilevel absorption machines
• Non-equilibrium Markov state modeling of periodically driven biomolecules
• Modeling of biomolecular machines in non-equilibrium steady states
• Non-Equilibrium Markov State Modeling of the Globule-Stretch Transition
• Thermodynamic inference in partially accessible Markov networks: A unifying perspective from transition-based waiting time distributions
• Markov State Modeling of Sliding Friction
• Performance of continuous quantum thermal devices indirectly connected to environments
• Waiting time distributions in hybrid models of motor-bead assays: A concept and tool for inference
• Geometric view of stochastic thermodynamics for non-equilibrium steady states