Isometric Uncertainty Relations

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.

15 pages, 2 figures

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• Thermodynamic uncertainty relation for Langevin dynamics by scaling time
• Symmetry-induced fluctuation relations for dynamical observables irrespective of their behaviour under time-reversal
• Fluctuation Relations associated to an arbitrary bijection in path space