Exact Distributions of Currents and Frenesy for Markov Bridges

Abstract

We consider discrete-time Markov bridges, chains whose initial and final states coincide. We derive exact finite-time formulae for the joint probability distributions of additive functionals of trajectories. We apply our theory to time-integrated currents and frenesy of enzymatic reactions, which may include absolutely irreversible transitions. We discuss the information that frenesy carries about the currents and show that bridges may violate known uncertainty relations in certain cases. Numerical simulations are in perfect agreement with our theory.

arXiv comment13 pages, 9 figures; accepted in Phys. Rev. E

References in corpus (56)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The large deviation approach to statistical mechanics
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Thermodynamic uncertainty relation for biomolecular processes
• Diffusion with Stochastic Resetting
• Dissipation bounds all steady-state current fluctuations
• Full Counting Statistics of Charge Transfer in Coulomb Blockade Systems
• First Passage Under Restart
• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• Single-electron current sources: towards a refined definition of ampere
• Direct evaluation of large-deviation functions
• Nonequilibrium Markov processes conditioned on large deviations
• Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
• Universal bounds on current fluctuations
• Speed Limit for Classical Stochastic Processes
• Finite-time generalization of the thermodynamic uncertainty relation
• Quantifying dissipation using fluctuating currents
• Stochastic resetting in backtrack recovery by RNA polymerases
• Current fluctuations and transport efficiency for general Langevin systems
• Discrete-time thermodynamic uncertainty relation
• Unravelling the large deviation statistics of Markovian open quantum systems
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Stochastic thermodynamics of resetting
• Stochastic Search with Poisson and Deterministic Resetting
• Kinetic uncertainty relation
• Nonequilibrium linear response for Markov dynamics, I: jump processes and overdamped diffusions
• First passage of a particle in a potential under stochastic resetting: a vanishing transition of optimal resetting rate
• Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes
• Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale
• A generalization of the thermodynamic uncertainty relation to periodically driven systems
• Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement
• Frenetic bounds on the entropy production
• Nonequilibrium Equalities in Absolutely Irreversible Processes
• Stochastic resetting in underdamped Brownian motion
• Continuous-time random walks with reset events: Historical background and new perspectives
• Hysteretic thermodynamic uncertainty relation for systems with broken time-reversal symmetry
• Local time of diffusion with stochastic resetting
• Unifying approach for fluctuation theorems from joint probability distributions
• Full Counting Statistics of Interacting Electrons
• Effective fluctuation and response theory
• Mapping of uncertainty relations between continuous and discrete time
• Sampling rare events across dynamical phase transitions
• Inequivalence of nonequilibrium path ensembles: the example of stochastic bridges
• Quantum Martingale Theory and Entropy Production
• Martingale theory for housekeeping heat
• Nonequilibrium Response and Frenesy
• An autonomous quantum machine to measure the thermodynamic arrow of time
• The Gibbs paradox revisited from the fluctuation theorem with absolute irreversibility
• Joint distributions of partial and global maxima of a Brownian Bridge
• Thermodynamic uncertainty for run-and-tumble type processes
• Statistical forces from close--to--equilibrium media
• Progressive quenching - Globally coupled model
• Area distribution and the average shape of a Lévy bridge
• Dispersion of the time spent in a state: General expression for unicyclic model and dissipation-less precision
• A case study of thermodynamic bounds for chemical kinetics

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