Journal of High Energy Physics

, 2016:106

A bound on chaos

  • Juan Maldacena
  • Stephen H. Shenker
  • Douglas Stanford
Open Access
Regular Article - Theoretical Physics

DOI: 10.1007/JHEP08(2016)106

Cite this article as:
Maldacena, J., Shenker, S.H. & Stanford, D. J. High Energ. Phys. (2016) 2016: 106. doi:10.1007/JHEP08(2016)106


We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λL ≤ 2πkBT/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.


1/N Expansion Black Holes AdS-CFT Correspondence 

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Juan Maldacena
    • 1
  • Stephen H. Shenker
    • 2
  • Douglas Stanford
    • 1
  1. 1.School of Natural SciencesInstitute for Advanced StudyPrincetonUSA
  2. 2.Stanford Institute for Theoretical Physics and Department of PhysicsStanford UniversityStanfordUSA

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