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.
27 pages, 4 figures
References in corpus (12)
- Dissipation: The phase-space perspective
- Ensemble and Trajectory Thermodynamics: A Brief Introduction
- Thermodynamics of feedback controlled systems
- Pathway Model, Superstatistics, Tsallis Statistics, and a Generalized Measure of Entropy
- Lower bounds on dissipation upon coarse graining
- Optimal protocols for minimal work processes in underdamped stochastic thermodynamics
- Hierarchical Bounds on Entropy Production Inferred from Partial Information
- Finite-time erasing of information stored in fermionic bits
- Role of measurement-feedback separation in autonomous Maxwell's demons
- First-passage times in renewal and nonrenewal systems
- 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