Violation of Local Detailed Balance Despite a Clear Time-Scale Separation

Abstract

Integrating out fast degrees of freedom is known to yield, to a good approximation, memory-less, i.e. Markovian, dynamics. In the presence of such a time-scale separation local detailed balance is believed to emerge and to guarantee thermodynamic consistency arbitrarily far from equilibrium. Here we present a transparent example of a Markov model of a molecular motor where local detailed balance can be violated despite a clear time-scale separation and hence Markovian dynamics. Driving the system far from equilibrium can lead to a violation of local detailed balance against the driving force. We further show that local detailed balance can be restored, even in the presence of memory, if the coarse-graining is carried out as Milestoning. Our work establishes Milestoning not only as a kinetically but for the first time also as a thermodynamically consistent coarse-graining method. Our results are relevant as soon as individual transition paths are appreciable or can be resolved.

12 pages, 5 figures. Minor corrections and new Supplemental Material

References in corpus (17)

• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• Thermodynamics of a physical model implementing a Maxwell demon
• Efficiency of cellular information processing
• Lower bounds on dissipation upon coarse graining
• Directed flow in non-adiabatic stochastic pumps
• Estimating entropy production from waiting time distributions
• Multiple-scale stochastic processes: decimation, averaging and beyond
• Fluctuation relations and coarse-graining
• Entropy production and coarse-graining in Markov processes
• Hierarchical Bounds on Entropy Production Inferred from Partial Information
• Coarse graining of master equations with fast and slow states
• Thermodynamic Uncertainty Relation Bounds the Extent of Anomalous Diffusion
• Thermodynamics of accuracy in kinetic proofreading: Dissipation and efficiency trade-offs
• Effective rates from thermodynamically consistent coarse-graining of models for molecular motors with probe particles
• Tightest bound on hidden entropy production from partially observed dynamics
• Local detailed balance across scales: from diffusions to jump processes and beyond
• Operationally Accessible Uncertainty Relations for Thermodynamically Consistent Semi-Markov Processes

Cited by in corpus (21)

• Milestoning estimators of dissipation in systems observed at a coarse resolution: When ignorance is truly bliss
• Thermodynamic cost for precision of general counting observables
• Fluctuating Entropy Production on the Coarse-Grained Level: Inference and Localization of Irreversibility
• General theory for localizing the where and when of entropy production meets single-molecule experiments
• Perspective: Time irreversibility in systems observed at coarse resolution
• Model-free inference of memory in conformational dynamics of a multi-domain protein
• On the emergence of memory in equilibrium versus non-equilibrium systems
• An estimator of entropy production for partially accessible Markov networks based on the observation of blurred transitions
• Entropy estimation for partially accessible Markov networks based on imperfect observations: Role of finite resolution and finite statistics
• Unified Linear Fluctuation-Response Theory Arbitrarily Far from Equilibrium
• Dynamics of Micro and Nanoscale Systems in the Weak-Memory Regime
• Dissipation at limited resolutions: Power law and detection of hidden dissipative scales
• Entropy production from waiting-time distributions for overdamped Langevin dynamics
• Evidence and quantification of memory effects in competitive first passage events
• Precisely controlled colloids: A playground for path-wise non-equilibrium physics
• Temperature-Dependent Dynamic Disproportionation in LiNiO${}_2$
• Dynamics of micro and nanoscale systems in the weak-memory regime: A mathematical framework beyond the Markov approximation
• Nonlinear Response Relations and Fluctuation-Response Inequalities for Nonequilibrium Stochastic Systems
• Purely quantum memory in closed systems observed via imperfect measurements
• Weak-Memory Dynamics in Discrete Time
• Entangled criticality and irreversibility in random Markov dynamics