Stochastic thermodynamics of interacting degrees of freedom: Fluctuation theorems for detached path probabilities

Abstract

Systems with interacting degrees of freedom play a prominent role in stochastic thermodynamics. Our aim is to use the concept of detached path probabilities and detached entropy production for bipartite Markov processes and elaborate on a series of special cases including measurement-feedback systems, sensors and hidden Markov models. For these special cases we show that fluctuation theorems involving the detached entropy production recover known results which have been obtained separately before. Additionally, we show that the fluctuation relation for the detached entropy production can be used in model selection for data stemming from a hidden Markov model. We discuss the relation to previous approaches including those which use information flow or learning rate to quantify the influence of one subsystem on the other. In conclusion, we present a complete framework with which to find fluctuation relations for coupled systems.

arXiv comment10 pages, 7 figures

References in corpus (27)

• Measuring Information Transfer
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Generalized Jarzynski Equality under Nonequilibrium Feedback Control
• Nonequilibrium Thermodynamics of Feedback Control
• The thermodynamics of prediction
• The Energetic Costs of Cellular Computation
• Thermodynamics with continuous information flow
• Nonequilibrium Detailed Fluctuation Theorem for Repeated Discrete Feedback
• First and Second Law of Thermodynamics at strong coupling
• Stochastic thermodynamics of bipartite systems: transfer entropy inequalities and a Maxwell's demon interpretation
• Thermodynamic costs of information processing in sensory adaption
• Efficiency of cellular information processing
• Information Thermodynamics on Causal Networks
• Maxwell's demon in biochemical signal transduction with feedback loop
• Second-law-like inequalities with information and their interpretations
• Universal Estimation of Directed Information
• Generalized detailed Fluctuation Theorem under Nonequilibrium Feedback control
• Sensory capacity: an information theoretical measure of the performance of a sensor
• Information-theoretic vs. thermodynamic entropy production in autonomous sensory networks
• Entropy production and time-asymmetry in the presence of strong interactions
• Thermodynamic limits to information harvesting by sensory systems
• Hidden Markov models for stochastic thermodynamics
• Probing small-scale intermittency with a fluctuation theorem
• Jarzynski-type equalities in gambling: role of information in capital growth
• Analogy Between Gambling and Measurement-Based Work Extraction
• Transfer-Entropy-Regularized Markov Decision Processes

Cited by in corpus (6)

• Quantum fluctuation theorems beyond two-point measurements
• Fluctuations of Apparent Entropy Production in Networks with Hidden Slow Degrees of Freedom
• Energetic cost of feedback control
• Hidden slow degrees of freedom and fluctuation theorems: an analytically solvable model
• Information Arbitrage in Bipartite Heat Engines
• Stochastic thermodynamics of a confined colloidal suspension under shear flow