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Thermodynamic interpretation to stochastic Fisher information and single-trajectory speed limits
Pedro B Melo1, Fernando Iemini2, Diogo O Soares-Pinto3
1Pontifícia Universidade Católica, Departamento de Física, Rio de Janeiro 22452-970, Rio de Janeiro, Brazil.
Physical Review. E
|August 19, 2025
Summary
The stochastic Fisher information (SFI) offers new thermodynamic interpretations and single-trajectory speed limits, distinct from the Fisher information. These findings reveal trajectory-level bounds in stochastic thermodynamics.
Area of Science:
- Thermodynamics
- Information Geometry
- Statistical Mechanics
Background:
- The Fisher information (FI) metric provides a geometric framework for stochastic thermodynamics, enabling calculations of thermodynamic lengths and deviations from equilibrium.
- The stochastic Fisher information (SFI) is a trajectory-level quantity related to the FI, which, on average, is equivalent to the FI.
Purpose of the Study:
- To elucidate the thermodynamic interpretation of the SFI.
- To investigate the existence of trajectory-level thermodynamic bounds.
- To explore the relationship between SFI, entropy production, and thermodynamic forces.
Main Methods:
- Analysis of the stochastic Fisher information (SFI) at the trajectory level.
- Derivation of thermodynamic interpretations and bounds for SFI.
- Application and testing of derived speed limits on Brownian particle models under varying drive forces.
Main Results:
- The thermodynamic interpretation of SFI depends solely on entropy produced and thermodynamic force, differing from FI.
- SFI enables the derivation of single-trajectory speed limits for Brownian particles.
- A hierarchy of average speed limits is derived from single-trajectory bounds, which are less tight than FI-derived limits.
Conclusions:
- SFI provides unique thermodynamic insights and trajectory-level speed limits.
- The derived hierarchy of average speed limits is validated by model simulations.
- This work opens new research directions for trajectory-level uncertainty relations in thermodynamics.
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