Ensemble and Trajectory Thermodynamics: A Brief Introduction

Abstract

We revisit stochastic thermodynamics for a system with discrete energy states in contact with a heat and particle reservoir.

Course given by C. Van den Broeck at the Summer School "Fundamental Problems in Statistical Physics XIII", June 16-29, 2013 Leuven, Belgium; V2: version accepted in Physica A (references improved + other minor changes)

References in corpus (22)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Path ensembles averages in systems driven far-from-equilibrium
• The Nonequilibrium Thermodynamics of Small Systems
• Entropy production as correlation between system and reservoir
• Universality of efficiency at maximum power
• Three detailed fluctuation theorems
• Optimal finite-time processes in stochastic thermodynamics
• Thermoelectric efficiency at maximum power in a quantum dot
• Quantum-dot Carnot engine at maximum power
• Efficiency at maximum power of Feynman's ratchet as a heat engine
• Strong bounds on Onsager coefficients and efficiency for three terminal thermoelectric transport in a magnetic field
• Efficiency of autonomous soft nano-machines at maximum power
• Reaching optimal efficiencies using nano-sized photo-electric devices
• Finite time thermodynamics for a single level quantum dot
• Fluctuation theorem for counting-statistics in electron transport through quantum junctions
• Thermodynamics of Quantum-Jump-Conditioned Feedback Control

Cited by in corpus (238)

• Fundamental aspects of steady-state conversion of heat to work at the nanoscale
• Irreversible entropy production, from quantum to classical
• Broken detailed balance and non-equilibrium dynamics in living systems
• Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions
• Nonequilibrium Thermodynamics of Chemical Reaction Networks: Wisdom from Stochastic Thermodynamics
• Fluctuation theorem uncertainty relation
• The unlikely Carnot efficiency
• Irreversibility in active matter systems: Fluctuation theorem and mutual information
• {\it Colloquium:} Statistical Mechanics and Thermodynamics at Strong Coupling: Quantum and Classical
• Quantum Thermodynamics: A Nonequilibrium Green's Functions Approach
• Discrete-time thermodynamic uncertainty relation
• Stochastic thermodynamics of computation
• Finite-time Landauer principle
• Inferring broken detailed balance in the absence of observable currents
• Uncertainty relations in stochastic processes: An information inequality approach
• Irreversible thermodynamics of open chemical networks I: Emergent cycles and broken conservation laws
• Efficiency statistics at all times: Carnot limit at finite power
• First and Second Law of Quantum Thermodynamics: A Consistent Derivation Based on a Microscopic Definition of Entropy
• Time-information uncertainty relations in thermodynamics
• Tightening the uncertainty principle for stochastic currents
• Non-Markovianity and negative entropy production rates
• The dissipation-time uncertainty relation
• Stochastic thermodynamics: From principles to the cost of precision
• Experimental Realization of a Minimal Microscopic Heat Engine
• Full counting statistics of vibrationally-assisted electronic conduction: transport and fluctuations of the thermoelectric efficiency
• Universal theory of efficiency fluctuations
• Stochastic thermodynamics in the strong coupling regime: An unambiguous approach based on coarse-graining
• Information Thermodynamics of Turing Patterns
• Power-efficiency-dissipation relations in linear thermodynamics
• Onsager coefficients in periodically driven systems
• Repeated interactions and quantum stochastic thermodynamics at strong coupling
• Collective power: Minimal model for thermodynamics of nonequilibrium phase transitions
• Play. Pause. Rewind. Measuring local entropy production and extractable work in active matter
• Conservation Laws shape Dissipation
• Thermodynamic Efficiency in Dissipative Chemistry
• Fluctuation-dissipation relations far from equilibrium
• Efficiency fluctuations in quantum thermoelectric devices
• Conservation Laws and Work Fluctuation Relations in Chemical Reaction Networks
• An operational approach to quantum stochastic thermodynamics
• Hysteretic thermodynamic uncertainty relation for systems with broken time-reversal symmetry
• Brownian duet: A novel tale of thermodynamic efficiency
• Unifying speed limit, thermodynamic uncertainty relation and Heisenberg principle via bulk-boundary correspondence
• Maximizing power and velocity of an information engine
• Thermodynamically Consistent Coarse Graining of Biocatalysts beyond Michaelis--Menten
• Stochastic thermodynamics of rapidly driven systems
• Entropy Production in Mesoscopic Stochastic Thermodynamics: Nonequilibrium Kinetic Cycles Driven by Chemical Potentials, Temperatures, and Mechanical Forces
• Second law of thermodynamics at stopping times
• Integral Fluctuation Relations for Entropy Production at Stopping Times
• Interlacing Relaxation and First-Passage Phenomena in Reversible Discrete and Continuous Space Markovian Dynamics
• Non-Markovian quantum thermodynamics: laws and fluctuation theorems
• Active matter under control: Insights from response theory
• Minimum energetic cost to maintain a target nonequilibrium state
• Work statistics in stochastically driven systems
• Thermodynamics of computing with circuits
• Thermodynamics of Chemical Waves
• Is stochastic thermodynamics the key to understanding the energy costs of computation?
• Thermodynamic uncertainty relation for first-passage times on Markov chains
• Overdamped stochastic thermodynamics with multiple reservoirs
• Metabolic constraints on synaptic learning and memory
• Quantum Trajectory Thermodynamics with Discrete Feedback Control
• Collective effects enhancing power and efficiency
• Nonequilibrium Thermodynamics of Non-Ideal Chemical Reaction Networks
• Effects of Quantum Coherence on Work Statistics
• Universality in driven Potts models
• Conservation laws and symmetries in stochastic thermodynamics
• Stochastic Efficiency for Effusion as a Thermal Engine
• Macroscopic Stochastic Thermodynamics
• Quantum Thermodynamics with Degenerate Eigenstate Coherences
• Efficiency of Single Particle Engines
• Dissipation in noisy chemical networks: The role of deficiency
• Uncertainty relation under information measurement and feedback control
• Detailed Fluctuation Theorems: A Unifying Perspective
• Tightest bound on hidden entropy production from partially observed dynamics
• Violation of Local Detailed Balance Despite a Clear Time-Scale Separation
• Energy and information flows in autonomous systems
• Thermodynamic costs of Turing Machines
• Irreversibility in active matter: General framework for active Ornstein-Uhlenbeck particles
• Jarzynski Equality, Crooks Fluctuation Theorem and the Fluctuation Theorems of Heat for Arbitrary Initial States
• Exact Distributions of Currents and Frenesy for Markov Bridges
• Martingales for physicists: A treatise on stochastic thermodynamics and beyond
• Uncertainty relations and fluctuation theorems for Bayes nets
• Finite-Time Thermodynamics of Fluctuations in Microscopic Heat Engines
• An autonomous quantum machine to measure the thermodynamic arrow of time
• Extreme reductions of entropy in an electronic double dot
• Stochastic Efficiency: Five Case Studies
• Stochastic thermodynamics of self-oscillations: the electron shuttle
• Work producing reservoirs: Stochastic thermodynamics with generalized Gibbs ensembles
• Stochastic thermodynamics of all-to-all interacting many-body systems
• Fluctuations of Apparent Entropy Production in Networks with Hidden Slow Degrees of Freedom
• Local detailed balance across scales: from diffusions to jump processes and beyond
• Thermodynamics of active matter: Tracking dissipation across scales
• Information thermodynamics for interacting stochastic systems without bipartite structure
• Probabilistically Violating the First Law of Thermodynamics in a Quantum Heat Engine
• The underdamped Brownian duet and stochastic linear irreversible thermodynamics
• Number of hidden states needed to physically implement a given conditional distribution
• Entropy production at criticality in a nonequilibrium Potts model
• Topologically-constrained fluctuations and thermodynamics regulate nonequilibrium response
• Thermodynamics of Quantum Causal Models: An Inclusive, Hamiltonian Approach
• Thermodynamics of Concentration vs Flux Control in Chemical Reaction Networks
• Nonequilibrium thermodynamics of the asymmetric Sherrington-Kirkpatrick model
• Maximal power for heat engines: role of asymmetric interaction times
• Stochastic discrete time crystals: Entropy production and subharmonic synchronization
• Double quantum dot coupled to a quantum point contact: A stochastic thermodynamics approach
• Model simplification and loss of irreversibility
• Dynamical phase transitions in the nonreciprocal Ising model
• Thermodynamics of Non-Elementary Chemical Reaction Networks
• Stochastic thermodynamics for a periodically driven single-particle pump
• Tuning nucleation kinetics via nonequilibrium chemical reactions
• Beyond Thermodynamic Uncertainty Relations: nonlinear response, error-dissipation trade-offs, and speed limits
• Functionals in stochastic thermodynamics: how to interpret stochastic integrals
• Stochastic thermodynamics with arbitrary interventions
• Methods and Conversations in (Post)Modern Thermodynamics
• Fluctuating Entropy Production on the Coarse-Grained Level: Inference and Localization of Irreversibility
• Classical emulation of quantum-coherent thermal machines
• Stochastic thermodynamics of a quantum dot coupled to a finite-size reservoir
• Landau theory for finite-time dynamical phase transitions
• Thermodynamic speed limits for mechanical work
• The Gibbs paradox revisited from the fluctuation theorem with absolute irreversibility
• Thermodynamics of collisional models for Brownian particles: General properties and efficiency
• Thermodynamics of the General Diffusion Process: Equilibrium Supercurrent and Nonequilibrium Driven Circulation with Dissipation
• Thermodynamic bounds on spectral perturbations, with applications to oscillations and relaxation dynamics
• Landauer Principle and Thermodynamics of Computation
• Entropy production of a Brownian ellipsoid in the overdamped limit
• Stochastic Thermodynamics of a Particle in a Box
• Nonequilibrium thermodynamic potentials for continuous-time Markov chains
• Energetic cost of feedback control
• Universal bounds on the performance of information-thermodynamic engine
• Maxwell's Demon walks into Wall Street: Stochastic Thermodynamics meets Expected Utility Theory
• Thermodynamically consistent model of an active Ornstein-Uhlenbeck particle
• Nonequilibrium interfacial properties of chemically driven fluids
• Reversal symmetries for cyclic paths away from thermodynamic equilibrium
• Stochastic thermodynamics of a probe in a fluctuating correlated field
• Effective thermodynamics of two interacting underdamped Brownian particles
• Length and sequence relaxation of copolymers under recombination reactions
• Stochastic thermodynamics based on incomplete information: Generalized Jarzynski equality with measurement errors with or without feedback
• Exact statistics and thermodynamic uncertainty relations for a periodically driven electron pump
• Nonequilibrium thermodynamics and information theory: Basic concepts and relaxing dynamics
• Local non-equilibrium thermodynamics
• Kinetics and thermodynamics of reversible polymerization in closed systems
• Autonomous demon exploiting heat and information at the trajectory level
• Efficiency fluctuations of small machines with unknown losses
• Thermodynamic aspects of nanoscale friction
• Fluctuation theorems in feedback-controlled open quantum systems: quantum coherence and absolute irreversibility
• Martingale structure for general thermodynamic functionals of diffusion processes under second-order averaging
• Biochemical Szilard engines for memory-limited inference
• Optimizing Brownian heat engine with shortcut strategy
• Non-Markovian Momentum Computing: Universal and Efficient
• General linear thermodynamics for periodically driven systems with multiple reservoirs
• Relation between topology and heat currents in multilevel absorption machines
• Free-energy transduction within autonomous systems
• Hyperaccurate bounds in discrete-state Markovian systems
• Thermodynamics of collective enhancement of precision
• Stochastic approach to entropy production in chemical chaos
• Maxwell's demon across the quantum-to-classical transition
• Entropy production and heat transport in harmonic chains under time dependent periodic drivings
• Thermodynamic performance of a periodically driven harmonic oscillator correlated with the baths
• Kinematic Basis of Emergent Energetics of Complex Dynamics
• Thermodynamic uncertainty relation from involutions
• Stochastic thermodynamics for kinetic equations
• Unlocking the potential of information flow: Maximizing free-energy transduction in a model of an autonomous rotary molecular motor
• On entropy production in nonequilibrium systems
• Nonlinear Stochastic Dynamics of Complex Systems, II: Potential of Entropic Force in Markov Systems with Nonequilibrium Steady State, Generalized Gibbs Function and Criticality
• Quality of the Thermodynamic Uncertainty Relation for Fast and Slow Driving
• Nonlinear Stochastic Dynamics of Complex Systems, I: A Chemical Reaction Kinetic Perspective with Mesoscopic Nonequilibrium Thermodynamics
• Entropy estimation for partially accessible Markov networks based on imperfect observations: Role of finite resolution and finite statistics
• Stochastic Impedance
• Fluctuation theorem for entropy production of a partial system in the weak coupling limit
• Mathematical foundation of nonequilibrium fluctuation-dissipation theorems for inhomogeneous diffusion processes with unbounded coefficients
• Minimum-dissipation principle for synchronised stochastic oscillators far from equilibrium
• Quantifying dissipation in flocking dynamics: When tracking internal states matters
• Stochastic thermodynamics of a confined colloidal suspension under shear flow
• Thermodynamics of majority-logic decoding in information erasure
• Energy fluctuations of a Brownian particle freely moving in a liquid
• Cooperativity, information gain, and energy cost during early LTP in dendritic spines
• Thermodynamic inference in partially accessible Markov networks: A unifying perspective from transition-based waiting time distributions
• Small-amplitude synchronisation in driven Potts models
• Dissipation in small systems: A Landau-Zener approach
• Characterization and optimization of heat engines: Pareto-optimal fronts and universal features
• Universal dynamic scaling in chemical reactions at and away from equilibrium
• Nonequilibrium thermodynamics of uncertain stochastic processes
• Information Dimension of Stochastic Processes on Networks: Relating Entropy Production to Spectral Properties
• Erasing a majority-logic bit
• Toward the nonequilibrium thermodynamic analog of complexity and the Jarzynski identity
• Information thermodynamics of financial markets: the Glosten-Milgrom model
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Thermodynamic cost of Brownian computers in the stochastic thermodynamics of resetting
• Performance of continuous quantum thermal devices indirectly connected to environments
• The Statistical Foundation of Entropy in Extended Irreversible Thermodynamics
• A Review of the System-Intrinsic Nonequilibrium Thermodynamics in Extended Space (MNEQT) with Applications
• Energy Storage in Steady States under Cyclic Local Energy Input
• A Thermodynamic Framework for Coherently Driven Systems
• A [3]-catenane non-autonomous molecular motor model: geometric phase, no-pumping theorem, and energy transduction
• Multi-scale model predicting friction of crystalline materials
• Inferring nonequilibrium thermodynamics from tilted equilibrium using information-geometric Legendre transform
• Stochastic paths controlling speed and dissipation
• Thermodynamic uncertainty relations for many-body systems with fast jump rates and large occupancies
• Hidden energy flows in strongly coupled nonequilibrium systems
• Dissipation in Hydrodynamics from Micro- to Macroscale: Wisdom from Boltzmann and Stochastic Thermodynamics
• Universal relations and bounds for fluctuations in quasistatic small heat engines
• Stochastic entropy production in the quiet Sun magnetic fields
• Minimal thermodynamic cost of communication
• Positional information trade-offs in boundary-driven reaction-diffusion systems
• Efficiency and power of minimally nonlinear irreversible heat engines with broken time-reversal symmetry
• Geometric view of stochastic thermodynamics for non-equilibrium steady states
• Work statistics at first-passage times
• Illusory cracks in the second law of thermodynamics in quantum nanoelectronics
• Noise and Thermodynamic Uncertainty Relation in "Underwater" Molecular Junctions
• Nonlinear Stochastic Dynamics of Complex Systems, III: Noneqilibrium Thermodynamics of Self-Replication Kinetics
• Stochastic thermodynamics for Ising chain and symmetric exclusion process
• Universal Ideal Behavior and Macroscopic Work Relation of Linear Irreversible Stochastic Thermodynamics
• Ternary Representation of Stochastic Change and the Origin of Entropy and Its Fluctuations
• Lecture notes on large deviations in non-equilibrium diffusive systems
• Superstatistics as the thermodynamic limit of driven classical systems
• Systematic analysis of critical exponents in continuous dynamical phase transitions of weak noise theories
• Uncertainty Relations for Mesoscopic Coherent Light
• On the energetic analysis of autonomous quantum systems
• A pedestrian's approach to large deviations in semi-Markov processes with an application to entropy production
• Fundamental precision limits in finite-dimensional quantum thermal machines
• A unified framework of unitarily residual measures for quantifying dissipation
• Thermodynamics of photoelectric devices
• Stochastic Thermodynamics of Learning Parametric Probabilistic Models
• Thermodynamics of fluctuations in small systems interacting with the environment
• Minimal entropy production due to constraints on rate matrix dependencies in multipartite processes
• N-States Continuous Maxwell Demon
• Fluctuation theorems for multiple co-evolving systems
• Work, entropy production, and thermodynamics of information under protocol constraints
• Iterative control strategies for non-linear systems
• Thermodynamic Circuits: Association of thermoelectric converters in stationary non-equilibrium
• Optimal control strategy for collisional Brownian engines
• Steady-state heat engines driven by finite reservoirs
• Entropic costs of extracting classical ticks from a quantum clock
• A Novel Dissipation Property of the Master Equation
• Fluctuation theorem in cavity quantum electrodynamics systems
• Quantum thermodynamics under continuous monitoring: a general framework
• Nonextensive Thermodynamics of the Morse Oscillator: Signature and Solid State Application
• Precision of an autonomous demon exploiting nonthermal resources and information
• Thermodynamics of nonequilibrium systems with uncertain parameters
• Dissipation and fluctuations of CMOS ring oscillators close to criticality