Classical Geometric Fluctuation Relations
arXiv:2410.23939 · doi:10.1088/1751-8121/add229
Abstract
Fisher Information (FI) is a quantity ubiquitously measured in such varied areas like metrology, machine learning, and biological complexity. Mathematically, it represents a lower bound in the variance of unknown parameters that are related to the distributions one has access, and a metric for probability manifolds. A stochastic analogous of the Fisher Information, dubbed stochastic Fisher Information was recently introduced in the literature by some of us. By exploring the probability distributions of the Stochastic Fisher Information (SFI), we uncover two fluctuation relations with an inherent geometric nature, as the SFI acts as a single nonequilibrium trajectory metric. The geometric nature of these relations is expressed through a stochastic length in entropy space derived from the system entropy associated with a nonequilibrium trajectory. We also explore the possibility of trajectory-dependent uncertainty relations linked to the SFI with time as a parameter. Finally, we test our geometric fluctuation relations using two nonequilibrium models.
15 pages, 1 figure; submitted to Journal of Physics A
References in corpus (27)
- The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
- Entropy production along a stochastic trajectory and an integral fluctuation theorem
- General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
- Steady State Thermodynamics of Langevin Systems
- Quantum Fisher information matrix and multiparameter estimation
- Fisher information and multiparticle entanglement
- Multipartite entanglement and high precision metrology
- Measuring thermodynamic length
- An Extension of the Fluctuation Theorem
- Fluctuation-Dissipation Theorem in Nonequilibrium Steady States
- Speed Limit for Classical Stochastic Processes
- Quantum Speed Limit is Not Quantum
- Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
- Uncertainty relations in stochastic processes: An information inequality approach
- Natural selection maximizes Fisher information
- Stochastic thermodynamic interpretation of information geometry
- Time-information uncertainty relations in thermodynamics
- Stochastic time-evolution, information geometry and the Cramer-Rao Bound
- The dissipation-time uncertainty relation
- Unified Approach to Classical Speed Limit and Thermodynamic Uncertainty Relation
- Quantum Fisher information measurement and verification of the quantum Cramér-Rao bound in a solid-state qubit
- Nonequilibrium uncertainty principle from information geometry
- Tighter thermodynamic bound on speed limit in systems with unidirectional transitions
- All electrical cooling of an optically levitated nanoparticle
- Exact Nonequilibrium Work Generating Function for a Small Classical System
- Tailoring bistability in optical tweezers with vortex beams and spherical aberration
- Stochastic thermodynamics of Fisher information