Revisiting the Mazur bound and the Suzuki equality

Abhishek Dhar, Aritra Kundu, Keiji Saito

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Among the few known rigorous results for time-dependent equilibrium correlations, important for understanding transport properties, are the Mazur bound and the Suzuki equality. The Mazur inequality gives a lower bound, on the long-time average of the time-dependent auto-correlation function of observables, in terms of equilibrium correlation functions involving conserved quantities. On the other hand, Suzuki proposes an exact equality for quantum systems. In this paper, we discuss the relation between the two results and in particular, look for the analogue of the Suzuki result for classical systems. This requires us to examine as to what constitutes a complete set of conserved quantities required to saturate the Mazur bound. We present analytic arguments as well as illustrative numerical results from a number of different systems. Our examples include systems with few degrees of freedom as well as many-particle integrable models, both free and interacting.

Original languageEnglish
Article number110618
JournalChaos, Solitons and Fractals
Publication statusPublished - 2021 Mar


  • Auto-correlation functions and ergodicity
  • Integrable systems
  • Mazur bound

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics


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