Stochastic thermodynamics: From principles to the cost of precision

Abstract

In these lecture notes, the basic principles of stochastic thermodynamics are developed starting with a closed system in contact with a heat bath. A trajectory undergoes Markovian transitions between observable meso-states that correspond to a coarse-grained description of, e.g., a biomolecule or a biochemical network. By separating the closed system into a core system and into reservoirs for ligands and reactants that bind to, and react with the core system, a description as an open system controlled by chemical potentials and possibly an external force is achieved. Entropy production and further thermodynamic quantities defined along a trajectory obey various fluctuation theorems. For describing fluctuations in a non-equilibrium steady state in the long-time limit, the concept of a rate function for large deviations from the mean behaviour is derived from the weight of a trajectory. Universal bounds on this rate function follow which prove and generalize the thermodynamic uncertainty relation that quantifies the inevitable trade-off between cost and precision of any biomolecular process. Specific illustrations are given for molecular motors, Brownian clocks and enzymatic networks that show how these tools can be used for thermodynamic inference of hidden properties of a system.

Lecture notes for the international summer school "Fundamental Problems in Statistical Physics" 2017 in Bruneck

References in corpus (14)

• The large deviation approach to statistical mechanics
• Thermodynamic uncertainty relation for biomolecular processes
• Universal trade-off between power, efficiency, and constancy in steady-state heat engines
• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
• Finite-time generalization of the thermodynamic uncertainty relation
• Discrete-time thermodynamic uncertainty relation
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Cost and Precision of Brownian Clocks
• Universal bound on the efficiency of molecular motors
• Universal Bound on the Fano Factor in Enzyme Kinetics
• Thermodynamic cost of external control
• Mapping current fluctuations of stochastic pumps to nonequilibrium steady states
• Microscopic heat from the energetics of stochastic phenomena

Cited by in corpus (72)

• Irreversibility in active matter systems: Fluctuation theorem and mutual information
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• Unified thermodynamic uncertainty relations in linear response
• Thermodynamic uncertainty relation in quantum thermoelectric junctions
• Thermodynamic uncertainty relations including measurement and feedback
• Effect of a magnetic field on the thermodynamic uncertainty relation
• Direct Route to Thermodynamic Uncertainty Relations and Their Saturation
• Thermodynamic uncertainty relation for systems with unidirectional transitions
• Entropy production in exactly solvable systems
• Thermodynamic Uncertainty Relation Bounds the Extent of Anomalous Diffusion
• Thermodynamic uncertainty relations for coherently driven open quantum systems
• Active Brownian particles driven by constant affinity
• Power, Efficiency and Fluctuations in a Quantum Point Contact as Steady-State Thermoelectric Heat Engine
• Efficiency fluctuations and noise induced refrigerator-to-heater transition in information engines
• Milestoning estimators of dissipation in systems observed at a coarse resolution: When ignorance is truly bliss
• How irreversible are steady-state trajectories of a trapped active particle?
• Kinetic Proofreading and the Limits of Thermodynamic Uncertainty
• Irreversibility in active matter: General framework for active Ornstein-Uhlenbeck particles
• Thermodynamic Bounds on Coherent Transport in Periodically Driven Conductors
• General bounds on electronic shot noise in the absence of currents
• Non-equilibrium thermodynamics of diffusion in fluctuating potentials
• Mathematical, Thermodynamical, and Experimental Necessity for Coarse Graining Empirical Densities and Currents in Continuous Space
• Information flow, Gating, and Energetics in dimeric molecular motors
• The nonequilibrium cost of accurate information processing
• Charge, spin, and heat shot noises in the absence of average currents: Conditions on bounds at zero and finite frequencies
• Reaching and violating thermodynamic uncertainty bounds in information engines
• Dissipation bounds precision of current response to kinetic perturbations
• Out-of-Equilibrium Fluctuation-Dissipation Bounds
• Improved bound on entropy production in a quantum annealer
• Thermodynamic Uncertainty Relations for Coherent Transport
• Flow of Energy and Information in Molecular Machines
• A thermodynamic uncertainty relation for a system with memory
• Thermodynamic bounds for diffusion in non-equilibrium systems with multiple timescales
• Exact statistics and thermodynamic uncertainty relations for a periodically driven electron pump
• Perspective: Time irreversibility in systems observed at coarse resolution
• Precision bound and optimal control in periodically modulated continuous quantum thermal machines
• Thermodynamic bounds on generalized transport: From single-molecule to bulk observables
• Modeling of biomolecular machines in non-equilibrium steady states
• Conceptual and practical approaches for investigating irreversible processes
• Stochastic thermodynamics and modes of operation of a ribosome: a network theoretic perspective
• Thermodynamic uncertainty relations in the presence of non-linear friction and memory
• Efficient large deviation estimation based on importance sampling
• Statistical features of systems driven by non-Gaussian processes: theory & practice
• Adaptive power method for estimating large deviations in Markov chains
• Numerical Study of the Thermodynamic Uncertainty Relation for the KPZ-Equation
• Pareto optimal fronts of kinetic proofreading
• Work relations with measurement and feedback control on nonuniform temperature systems
• Nonlinear response theory of molecular machines
• Universal dynamic scaling in chemical reactions at and away from equilibrium
• Homeostatic and Adaptive Energetics: Nonequilibrium Fluctuations Beyond Detailed Balance in Voltage-Gated Ion Channels
• On correlations and fluctuations of time-averaged densities and currents with general time-dependence
• Assembly of heteropolymers via a network of reaction coordinates
• Waiting time distributions in hybrid models of motor-bead assays: A concept and tool for inference
• Feynman-Kac theory of time-integrated functionals: Itô versus functional calculus
• Heat production in a stochastic system with nonlinear time-delayed feedback
• Quantum stochastic thermodynamics in the mesoscopic-leads formulation
• First and Second Laws of Information Processing by Nonequilibrium Dynamical States
• Minimal thermodynamic cost of communication
• Apparent violations of the second law in the quantum-classical dynamics of interacting levitated nanoparticles
• Full counting statistics and first-passage times in quantum Markovian processes: Ensemble relations, metastability, and fluctuation theorems
• Geometric view of stochastic thermodynamics for non-equilibrium steady states
• Stochastic Thermodynamics at the Quantum-Classical Boundary: A Self-Consistent Framework Based on Adiabatic-Response Theory
• Uncertainty Relations for Mesoscopic Coherent Light
• Current noise in quantum dot thermoelectric engines
• Multiple Pareto-optimal solutions of the dissipation-adaptation trade-off
• Tightening the thermodynamic uncertainty relations with null-entropy events: What we learn when nothing happens
• Topological constraints on self-organisation in locally interacting systems
• On the lower bound of the Heisenberg uncertainty product in the Boltzmann states
• Optimizing Energetic cost of Uncertainty in a Driven System With and Without Feedback
• Thermodynamic uncertainty relation in the overdamped limit with a magnetic Lorentz force
• Patterns that persist: Heritable information in stochastic dynamics