Stochastic thermodynamics with arbitrary interventions

Abstract

We extend the theory of stochastic thermodynamics in three directions: (i) instead of a continuously monitored system we consider measurements only at an arbitrary set of discrete times, (ii) we allow for imperfect measurements and incomplete information in the description, and (iii) we treat arbitrary manipulations (e.g. feedback control operations) which are allowed to depend on the entire measurement record. For this purpose we define for a driven system in contact with a single heat bath the four key thermodynamic quantities: internal energy, heat, work and entropy along a single `trajectory' for a causal model. The first law at the trajectory level and the second law on average is verified. We highlight the special case of Bayesian or `bare' measurements (incomplete information, but no average disturbance) which allows us to compare our theory with the literature and to derive a general inequality for the estimated free energy difference in Jarzynksi-type experiments. An analysis of a recent Maxwell demon experiment using real-time feedback control is also given. As a mathematical tool, we prove a classical version of Stinespring's dilation theorem, which might be of independent interest.

arXiv comment13 + 2 pages incl. 2 Figures and References. Extended and improved version

References in corpus (36)

• A nonequilibrium equality for free energy differences
• Measuring Information Transfer
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• The Nonequilibrium Thermodynamics of Small Systems
• Stochastic thermodynamics under coarse-graining
• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• Non-Markovian quantum processes: complete framework and efficient characterisation
• Work and information processing in a solvable model of Maxwell's demon
• Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions
• Operational Markov condition for quantum processes
• Information processing and the second law of thermodynamics: an inclusive, Hamiltonian approach
• The role of quantum measurement in stochastic thermodynamics
• An experimental test of the Jarzynski equality in a mechanical experiment
• Information-theoretic approach to the study of control systems
• Information Thermodynamics on Causal Networks
• Stochastic thermodynamics of computation
• Large work extraction and the Landauer limit in a continuous Maxwell demon
• Stochastic thermodynamics of single enzymes and molecular motors
• Non-Markovianity and negative entropy production rates
• Stochastic thermodynamics for "Maxwell demon" feedbacks
• Effective thermodynamics for a marginal observer
• Repeated interactions and quantum stochastic thermodynamics at strong coupling
• Probing the power of an electronic Maxwell Demon
• Entropy production and fluctuation theorems for Langevin processes under continuous non-Markovian feedback control
• Above and Beyond the Landauer Bound: Thermodynamics of Modularity
• An operational approach to quantum stochastic thermodynamics
• Stochastic thermodynamics of Langevin systems under time-delayed feedback control: I. Second-law-like inequalities
• Heat flow due to time-delayed feedback
• Effective fluctuation and response theory
• Hidden Markov models for stochastic thermodynamics
• Thermodynamics of Quantum-Jump-Conditioned Feedback Control
• Free energy inference from partial work measurements in small systems
• Stochastic thermodynamics based on incomplete information: Generalized Jarzynski equality with measurement errors with or without feedback
• Thermodynamic inference based on coarse-grained data or noisy measurements

Cited by in corpus (20)

• Quantum stochastic processes and quantum non-Markovian phenomena
• Quantum fluctuation theorems beyond two-point measurements
• Repeated interactions and quantum stochastic thermodynamics at strong coupling
• When is a non-Markovian quantum process classical?
• An operational approach to quantum stochastic thermodynamics
• Work as an external quantum observable and an operational quantum work fluctuation theorem
• Experimental assessment of entropy production in a continuously measured mechanical resonator
• Entropy Production in Continuously Measured Gaussian Quantum Systems
• Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force
• Resource theories of multi-time processes: A window into quantum non-Markovianity
• Thermodynamics of Quantum Causal Models: An Inclusive, Hamiltonian Approach
• Exponential improvement for quantum cooling through finite-memory effects
• Informational steady-states and conditional entropy production in continuously monitored systems
• Non-Markovian Memory Strength Bounds Quantum Process Recoverability
• Relaxation of Multitime Statistics in Quantum Systems
• Memory Effects in Quantum Processes
• Informational steady-states and conditional entropy production in continuously monitored systems: the case of Gaussian systems
• Partially Observable Szilard Engines
• Experimentally probing entropy reduction via iterative quantum information transfer
• First Law of Quantum Thermodynamics in a Driven Open Two-Level System