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Quantum bounds and fluctuation-dissipation relations

by Silvia Pappalardi, Laura Foini, Jorge Kurchan

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Submission summary

Authors (as registered SciPost users): Laura Foini · Silvia Pappalardi
Submission information
Preprint Link:  (pdf)
Date accepted: 2022-03-31
Date submitted: 2021-12-14 11:14
Submitted by: Pappalardi, Silvia
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
  • Quantum Physics
Approach: Theoretical


In recent years, there has been intense attention on the constraints posed by quantum mechanics on the dynamics of the correlation at low temperatures, triggered by the postulation and derivation of quantum bounds on the transport coefficients or on the chaos rate. However, the physical meaning and the mechanism enforcing such bounds is still an open question. Here, we discuss the quantum fluctuation-dissipation theorem (the KMS conditions) as the principle underlying bounds on correlation time scales. By restating the problem in a replicated space, we show that the quantum bound to chaos is a direct consequence of the KMS condition, as applied to a particular pair of two-time correlation and response functions. Encouraged by this, we describe how quantum fluctuation-dissipation relations act in general as a blurring of the time-dependence of correlations, which can imply bounds on their decay rates. Thinking in terms of fluctuation-dissipation opens a direct connection between bounds and other thermodynamic properties.

Published as SciPost Phys. 12, 130 (2022)

Reports on this Submission

Anonymous Report 1 on 2022-1-25 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2110.03497v3, delivered 2022-01-25, doi: 10.21468/SciPost.Report.4241


1. The authors use the formalism of the fluctuation-dissipation theorem in a novel way to illuminate bounds on exponential growth and decay rates of correlation and response functions.

2. By working directly in the time domain, some issues that were problematic in the frequency domain are resolved.

3. The formalism is innovative and should prove useful in broader contexts.

4. The paper is very clearly written.




This is an extremely interesting and potentially quite important paper. It definitely meets the criterion of opening a new pathway in an existing esearch direction, with clear potential for multipronged follow-up work.

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  • formatting: excellent
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