Hidden Markov models for stochastic thermodynamics

Abstract

The formalism of state estimation and hidden Markov models (HMMs) can simplify and clarify the discussion of stochastic thermodynamics in the presence of feedback and measurement errors. After reviewing the basic formalism, we use it to shed light on a recent discussion of phase transitions in the optimized response of an information engine, for which measurement noise serves as a control parameter. The HMM formalism also shows that the value of additional information shows a maximum at intermediate signal-to-noise ratios. Finally, we discuss how systems open to information flow can apparently violate causality; the HMM formalism can quantify the performance gains due to such violations.

27 pages, 13 figures; submitted to New J. Phys

References in corpus (5)

• High-precision test of Landauer's principle in a feedback trap
• Work and information processing in a solvable model of Maxwell's demon
• Thermodynamics of feedback controlled systems
• Stochastic thermodynamics with information reservoirs
• Finite-time erasing of information stored in fermionic bits

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• Effective fluctuation and response theory
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• Continuous information flow fluctuations
• Shannon Entropy Rate of Hidden Markov Processes
• Stochastic thermodynamics with arbitrary interventions
• Energetic cost of feedback control
• Divergent Predictive States: The Statistical Complexity Dimension of Stationary, Ergodic Hidden Markov Processes
• Stochastic thermodynamics based on incomplete information: Generalized Jarzynski equality with measurement errors with or without feedback
• Fraudulent White Noise: Flat power spectra belie arbitrarily complex processes
• Spectral Simplicity of Apparent Complexity, Part I: The Nondiagonalizable Metadynamics of Prediction
• Non-Markovian Momentum Computing: Universal and Efficient
• Dynamics of switching processes: general results and applications to intermittent active motion
• Measurement-Induced Randomness and Structure in Controlled Qubit Processes
• Information Arbitrage in Bipartite Heat Engines
• Stochastic thermodynamics of interacting degrees of freedom: Fluctuation theorems for detached path probabilities
• Manipulating hidden-Markov-model inferences by corrupting batch data
• When memory pays: Discord in hidden Markov models
• Information in feedback ratchets
• Partially Observable Szilard Engines
• Nonequilibrium thermodynamics of uncertain stochastic processes
• Ambiguity Rate of Hidden Markov Processes
• Constrained hidden Markov models reveal further Hsp90 protein states
• Optimality and Complexity in Measured Quantum-State Stochastic Processes
• Phase transition for parameter learning of Hidden Markov Models