Isometric Uncertainty Relations

Hadrien Vroylandt, Karel Proesmans, Todd R. Gingrich*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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→ ∞ 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.

Original languageEnglish (US)
Pages (from-to)1039-1053
Number of pages15
JournalJournal of Statistical Physics
Issue number4
StatePublished - Feb 1 2020


  • Broken symmetry
  • Isometric fluctuation theorem
  • Nonequilibrium steady state
  • Thermodynamic uncertainty relation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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