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

References in corpus (8)

• Thermodynamic uncertainty relation for biomolecular processes
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Discrete-time thermodynamic uncertainty relation
• Cost and Precision of Brownian Clocks
• Thermodynamic uncertainty relation in quantum thermoelectric junctions
• Symmetries in Fluctuations Far from Equilibrium
• Isometric fluctuation relations for equilibrium states with broken symmetry
• Thermodynamic bounds on equilibrium fluctuations of a global or local order parameter