Isometric Uncertainty Relations

TL;DR

This paper derives a generalized bound on flux variance based on isometric fluctuation theorems, connecting fluctuation relations with thermodynamic uncertainty principles across different system dimensions.

Contribution

It introduces a new dimension-dependent bound on flux variance that interpolates between known thermodynamic uncertainty relations, extending their applicability.

Findings

The bound depends on system dimension d and interpolates between known limits.

The relation is applicable to order parameters in equilibrium systems.

Illustrated on a Heisenberg spin chain.

Abstract

We generalize the link between fluctuation theorems and thermodynamic uncertainty relations by deriving a bound on the variance of fluxes that satisfy an isometric fluctuation theorem. The resulting bound, which depends on the system's dimension $d$, naturally interpolates between two known bounds. The bound derived from the entropy production fluctuation theorem is recovered for $d=1$, and the original entropy production thermodynamic uncertainty relation is obtained in the $d \to \infty$ limit. We show that our result can be generalized to order parameters in equilibrium systems, and we illustrate the results on a Heisenberg spin chain.