Thermodynamic interpretation to Stochastic Fisher Information and Single-Trajectory Speed Limits

Abstract

The Fisher information (FI) metric is a Riemannian metric that allows a geometric treatment of stochastic thermodynamics, introducing the possibility of computing thermodynamic lengths and deviations from equilibrium. At the trajectory level, a related quantity can be introduced, the stochastic Fisher information (SFI), which on average, is equivalent to the FI. In this work, we discuss two fundamental questions regarding the SFI; namely, (i) what is the thermodynamic interpretation to the SFI, and (ii) are there any trajectory-level thermodynamic bounds . We find that, contrary to previous results in the literature for the FI, the thermodynamic interpretation of the SFI depends only on the entropy produced by the system and on the thermodynamic force. Moreover, we find that the SFI allows one to derive single-trajectory speed limits, which we demonstrate to hold for a Brownian particle under a saturating drive force and a Brownian particle under a decreasing drive force. From the ensemble of single-trajectory bounds, one can derive a hierarchy of average speed limits that are always less tight than the one derived from the FI. We test our results for speed limits on the adopted models and find that the hierarchy of average speed limits is respected and that the single-trajectory speed limits behave qualitatively similar to the average and stochastic speed limits, with some trajectories achieving velocities higher than the tightest average bound whenever it does not saturate. Our results open avenues for the exploration of uncertainty relations at the trajectory level.

arXiv comment13 pages, 7 figures

References in corpus (38)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• Thermodynamic uncertainty relation for biomolecular processes
• General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
• Dynamical ensembles in stationary states
• Quantum Fisher information matrix and multiparameter estimation
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Multipartite entanglement and high precision metrology
• Quantum speed limit for physical processes
• Quantum speed limits in open system dynamics
• Measuring thermodynamic length
• Irreversible entropy production, from quantum to classical
• Experimental reconstruction of work distribution and verification of fluctuation relations at the full quantum level
• Thermodynamic metrics and optimal paths
• The Three Faces of the Second Law: I. Master Equation Formulation
• Fluctuation Theorems
• Generalized Geometric Quantum Speed Limits
• Speed Limit for Classical Stochastic Processes
• Quantum Speed Limits Across the Quantum-to-Classical Transition
• Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
• Quantum Speed Limit is Not Quantum
• Reversing the direction of heat flow using quantum correlations
• Stochastic thermodynamic interpretation of information geometry
• Stochastic time-evolution, information geometry and the Cramer-Rao Bound
• 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
• Far-from-Equilibrium Measurements of Thermodynamic Length
• Floquet time-crystals as sensors of AC fields
• Nonequilibrium uncertainty principle from information geometry
• Tighter thermodynamic bound on speed limit in systems with unidirectional transitions
• Information geometry approach to quantum stochastic thermodynamics
• Quantum speed limit for states and observables of perturbed open systems
• Stochastic thermodynamics of Fisher information
• Classical Geometric Fluctuation Relations