{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"48cc6199758f2a3d5ea371d0213ac902fac639399c144f545972857f96d61e60","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["bc4d842ed0f40662367ce8a3aba75d31512a0753eba1e84123bcf05194e0cf71","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"c67205b782224b187672dd0e2e7454e696c49b0691ffda63a0eff33b1ae2f2dd","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"cm.chaos-scrambling.diffusion-butterfly-bound","kind":"well-posed","literature_status":"partially-resolved","n":"2","parents":[],"plain":"In some theories, how fast heat spreads is limited by how fast chaos spreads. Whether this limit holds in every chaotic lattice system is not settled.","posed_since":"2016","precise":"Blake (2016) found $D = C v_B^2/(2 \\pi k_B T/\\hbar)$ with $C$ of order one in holographic theories, where $v_B$ is the butterfly velocity of the OTOC front; its charge-diffusion form fails in inhomogeneous holographic models (Lucas and Steinberg 2016). Hartman, Hartnoll and Mahajan (2017) conjectured an upper bound $D <\\sim v^2 \\tau_{\\mathrm{eq}}$ ($v$ a characteristic velocity, $\\tau_{\\mathrm{eq}}$ the local equilibration time), and in inhomogeneous SYK chains energy diffusion obeys $D \\le v_B^2/\\lambda_L$ (Gu, Lucas, Qi 2017). For local chaotic lattice systems with a well-defined Lyapunov regime, does $D_{\\mathrm{energy}} \\le C v_B^2/\\lambda_L$ hold with a universal $C$ of order one? Answer yes or no, with a counterexample or derivation.","problem_ref":"bc4d842ed0f40662367ce8a3aba75d31512a0753eba1e84123bcf05194e0cf71","references":"","settled_by":"A general derivation from hydrodynamics and operator growth, or an explicit lattice model with $D_{\\mathrm{energy}}\\,\\lambda_{\\mathrm{L}}/v_{\\mathrm{B}}^2 \\to \\infty$.","status_note":"The upper bound holds in holographic models and inhomogeneous SYK chains, and the charge-diffusion version has counterexamples; the general lattice case is open.","title":"Is energy diffusion bounded above by the butterfly 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