{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"edd0684418b41ee819b32610bddd64e8a0ea7ad5477602486a29661dd1ab8f1c","created":"2026-10-03T07:17:58Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"1c48dcf8778c0e15981c7ffb22a02f17348e7c15f8460ad9cd368839f9dbff36","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":"1","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":null,"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 velocity","topic_ref":"c681d6b7c25d1a7c6ef6a216819426033bd04126d74656c004cc4a70c0ac92e1"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"bc4d842ed0f40662367ce8a3aba75d31512a0753eba1e84123bcf05194e0cf71","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"640c3caad3bd1ed5aa79c01e491664684033e3da46bb51cb6ba78672c7e92e1b","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"mvmIWyKrc9CE-VS_rTGRfwybsX7khUe7tS1FFw-C2IGJmqjQ898sJwNKEStJoZxzGZitSfmacVxMU6vHQFNoBA"},"schema":"pubphys.envelope/1"},"record_hash":"bc4d842ed0f40662367ce8a3aba75d31512a0753eba1e84123bcf05194e0cf71","leaf_index":915}