Nonequilibrium thermodynamics of uncertain stochastic processes
arXiv:2210.05249 · doi:10.1103/PhysRevResearch.6.013021
Abstract
Stochastic thermodynamics is formulated under the assumption of perfect knowledge of all thermodynamic parameters. However, in any real-world experiment, there is non-zero uncertainty about the precise value of temperatures, chemical potentials, energy spectrum, etc. Here we investigate how this uncertainty modifies the theorems of stochastic thermodynamics. We consider two scenarios: in the (called \emph{effective}) scenario we fix the (unknown, randomly generated) experimental apparatus and then repeatedly observe (stochastic) trajectories of the system for that fixed apparatus. In contrast, in a (called \emph{phenomenological}) scenario the (unknown) apparatus is re-generated for each trajectory. We derive expressions for thermodynamic quantities in both scenarios. We also discuss the physical interpretation of effective (scenario) entropy production (EP), derive the effective mismatch cost, and provide a numerical analysis of the effective thermodynamics of a quantum dot implementing bit erasure with uncertain temperature. We then analyze the protocol for moving between two state distributions that maximize effective work extraction. Next, we investigate the effective thermodynamic value of information, focusing on the case where there is a delay between the initialization of the system and the start of the protocol. Finally, we derive the detailed and integrated fluctuation theorems (FTs) for the phenomenological EP. In particular, we show how the phenomenological FTs account for the fact that the longer a trajectory runs, the more information it provides concerning the precise experimental apparatus, and therefore the less EP it generates.
arXiv comment27 pages, 4 figures
References in corpus (38)
- Stochastic thermodynamics, fluctuation theorems, and molecular machines
- Superstatistics
- Dissipation: The phase-space perspective
- Entropy production as correlation between system and reservoir
- Minimal Energy Cost for Thermodynamic Information Processing: Measurement and Information Erasure
- Ensemble and Trajectory Thermodynamics: A Brief Introduction
- The Three Faces of the Second Law: I. Master Equation Formulation
- Nonequilibrium Thermodynamics of Feedback Control
- Estimating dissipation from single stationary trajectories
- Entropy production and the arrow of time
- First and Second Law of Thermodynamics at strong coupling
- {\it Colloquium:} Statistical Mechanics and Thermodynamics at Strong Coupling: Quantum and Classical
- Semantic information, autonomous agency, and nonequilibrium statistical physics
- Thermodynamics of feedback controlled systems
- Pathway Model, Superstatistics, Tsallis Statistics, and a Generalized Measure of Entropy
- Stochastic thermodynamics of computation
- Lower bounds on dissipation upon coarse graining
- Generalized entropies and the transformation group of superstatistics
- Optimal protocols for minimal work processes in underdamped stochastic thermodynamics
- Stochastic thermodynamics in the strong coupling regime: An unambiguous approach based on coarse-graining
- Generalization of the Second Law for a Nonequilibrium Initial State
- Role of Mutual Information in Entropy Production under Information Exchanges
- Hierarchical Bounds on Entropy Production Inferred from Partial Information
- Finite-time erasing of information stored in fermionic bits
- Stretched exponentials from superstatistics
- Role of measurement-feedback separation in autonomous Maxwell's demons
- Bayesian approach to superstatistics
- Thermodynamics of computing with circuits
- Hidden Markov models for stochastic thermodynamics
- Dependence of dissipation on the initial distribution over states
- First-passage times in renewal and nonrenewal systems
- Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force
- Initial-State Dependence of Thermodynamic Dissipation for any Quantum Process
- Quantum trajectory analysis of single microwave photon detection by nanocalorimetry
- Temperature is not an observable in superstatistics
- Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes
- Entropy production and heat capacity of systems under time-dependent oscillating temperature
- Comment on "Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force"