{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"b36f1185f7a42875eae1b913e5a7c1cc40ee1f77e90f470459d585bd73e4092e","created":"2026-10-03T07:18:11Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"cd1dacef58e8898a4879d6f71de9a04bcd5f55ec77e940c70963b9db0a45585d","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"stat.mpemba-relaxation.critical-universality","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Near a phase transition (such as a magnet losing its magnetization at a critical temperature), relaxation becomes slow and governed by a few universal numbers. The question is whether the existence and timing of Mpemba effects there are also fixed by those universal numbers.","posed_since":"","precise":"Ising-class system with non-conserved order parameter (Glauber or model-A dynamics), bath temperature $T_{\\mathrm{b}}$ near the critical temperature $T_{\\mathrm{crit}}$, initial equilibrium at $T_{0}$. Using a stated distance from final equilibrium, determine whether the existence of direct $\\left(T_{0} > T_{\\mathrm{b}}\\right)$ and inverse $\\left(T_{0} < T_{\\mathrm{b}}\\right)$ Mpemba effects and the crossing time $t_{x}$ obey scaling forms $t_{x} \\sim \\left|T_{\\mathrm{b}} - T_{\\mathrm{crit}}\\right|^{-\\nu z} F\\left(\\left(T_{0} - T_{\\mathrm{crit}}\\right)/\\left(T_{\\mathrm{b}} - T_{\\mathrm{crit}}\\right)\\right)$ set by the static exponent $\\nu$, the dynamic exponent $z$ and the order of the transition, independent of lattice and microscopic rates. The answer is a classification of where each effect occurs, with the scaling function $F$ or a demonstration that none exists.","problem_ref":null,"references":"","settled_by":"Large-scale Monte Carlo or renormalization-group computation across several models of one universality class showing a common F and common boundaries for direct and inverse effects.","status_note":"A Landau theory predicts Mpemba effects at phase transitions (Holtzman and Raz 2022), and Monte Carlo work on Ising and Potts models reports a scaling picture, set by the initial-state correlation length, that holds across first- and second-order transitions (Chatterjee et al., arXiv:2309.03709); no scaling function $F$ in terms of $\\nu$ and $z$ with RG or multi-model confirmation has been established (2026).","title":"Universal scaling of direct and inverse Mpemba effects near criticality","topic_ref":"b9dc5bd92d3519c9f31327e4098f8e26bf4890131f68cb53d43d3834030d1d0c"},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"5755725e511243a3280279f58b4c7328c0b7390d5cf5913a50e970037511b009","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"210c21abfa88484e46df3ccac4733a76ae26a1e0f2ea33bb6fb2ce380d3461f4","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"XmM3gbRtGUc52q9ha9VpPW7mkLXl4RLAeywoShvH8iStJ11nQbmgqTK4lcpfzmfybI-kTic-lbPUnLcbJWGSCA"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIIQwhq_qISE5G3zzKxHM6dq4moeDy6jO7b7LOOA00YfTwICEWunLgBXRN6CiXjMTl3U_wTOFyIhZUcfMxMP6WqUurCPAg26upOKJGCZjYl0ciuDnCAciGmTdozsjmfis3yqduHrwI8SDHQVPr3Oc_hq0pLB7AcOSkW0bh3Wft92NKbRBqoj-8XwjxIBzWAdcFihjfOAo-UGPPt8av0Pq2c8ZUorGiPuzhbbZqCPEgzrQdyyaqW1zE1X4trLrb_6E0B6Rdaa5Wdx4nyuyma0wI8CAS78GmgPwAiurRrYkxxnm68OnBs1klo2akMuijCYfa8wjwILmTsItrvjIMksEGgssyK3U7WUtlZ03fFlSkoJQy4c9JCPAg9GXDiYzI_6rOj17scwJEh5LD70yT4n2onsKSe2X_YAUI8CDhHjTRDsgFglT04grMuKx-URV-Za14ktgMuGI-MgavMgjxINIT2A3d_DeKxwK521mnlCvK2wl2UdXYsWFx2YY9xgr-CPAg3v2QXfNkDO6Xzu9061umH0rhjRfHBKza3uG2nPQbpd8I8CCtNZgmApuKULvPC9nsMCaM05arV-F3o5FTlnJCnRvdMgjwIBGYo5Vxy-d7U5zKv5vp3Ii7hJPH_BDLCzA13c47p9q7CP_wCHbghVgOFMuNCPAQPZK2lHbTMqcCYUotzOQcmQjwIJ7ruRIs6HnufKxCpmLUgeUl0aUu0ov4_3PqcppS-bddCPEgI530vHzdwz_3o9jYQ3WablSaV64Wfn7Pmby5WLyI-A0I8QRqwKw78AhITF7Tr3a1xP8Ag9_jDS75DI4sK2h0dHBzOi8vYm9iLmJ0Yy5jYWxlbmRhci5vcGVudGltZXN0YW1wcy5vcmcI8CBXWeNiWFWltfHE0nkDXsVKIykUUwuObhsnN-2fvBt98gjwIM5Vf7j68sOFgVysYMc5S09Hho-fqxYW3oQ4oKUX7JpPCPAgaKHHQB3sdd9w1hu4NMh7vmb-p0X2r4uyVKKCj1G7S28I8SAW2Mg6Bzi9ygjrrjIYB7w90fwMcxH24SsqLmzPyAMGfwjwIMQ863zlveYIpNKWVrZaDOa4vowwoOg2CcTW8gXtxK3dCPEgrZxGGAf-t8jhz_eLMUyBN1IhNrdYDRcNHWvQcwNG9woI8CCVOUHG1YXudbaFIgUYvrCIevRWvb2ubhQAo-z0duD0rQjxIDBeKerVGkO3J2eXDwdraSioXbIWsdIPEN1s8pIwJIS2CPAgV2kB3n3JZ5HwBQjpRL1CWKnqvdCjZk3RcALk6N2wHigI8CB-wbljNlfqElD25uZkNg6taS81YDRU2vfMqGVQ420O9AjxWQEAAAABJM43UU6MLMRrPlCUqossvu1q_knons5yylyWTgxZzWUAAAAAAP7___8CLgABAAAAAAAWABQrYt3E7OllKRCEmL3FL589l78_5wAAAAAAAAAAImog8ATiyw4ACAjxILmbcIO7ixv3pCtwUMZ1VQGKus54F9lZ8-w5ECD5ZuiICAjwIG6ynCyFTLPE7Rgk-0ZGCtBDyqNQx8YvaSZNHy8D8p8jCAjwIMX8zoD2Be1YWvcx_bexVPRmBX0hK-do8b8t9SarimQVCAjxIG6XtpqIEclLlhzcK1LVjqoPGrjjmLnyno8tcETMzECECAjwIF6mlfXOFY51JhrK4eze8zQlKV75OYZYqbtyi8BWxmAsCAjwIKKUcJmVoz-u-geiRV_-ZHdF0VEPXaEPFWf_JX_0e7G2CAjxIGMeD0Z5QWNKBcAEpHht007FFIILW6aSJ8f3CMkKNsneCAjwIBFr6Je8rkB7kwhPGbq0yRgFwZsvW9JhY5sXDRtrq0QwCAjwIAHAwXaus-yUgKICJB5mVvx8VZuJgjwnpb0qWPg1pi6DCAjxIAJhb8cefkVHTAMymdsxa-_i-tUua62LcpALQnPG7R9_CAjwIDvsFqBhPfAL6TCtXZd7gBWmMpx6iiZ-Ug0Jf_LlcstgCAjwIDJRBX6Q0Vge-ra-k1_g76yJWTEp6WWF13I3JpTnsZPJCAjwILykZCbkC9VQgl5gytPKKir6T9nTvKR6y05iWSHBTQgzCAgABYiWDXPXGQED45c78Ah-sGbmQAwfZwjwEAYqxtHnZiPZnJEGPx_JvKsI8SDXkqDg17YsZIrEz5acRx7mBXCKW5mKNgRYnw_-U2cpDgjxBGrArDrwCEfK6Mono428_wCD3-MNLvkMji4taHR0cHM6Ly9hbGljZS5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3JnCPAg10nyJ6Jn4kshQQQCKE0Lvj3hBC6nLRBVIzaPV4eh8VwI8CCQaAqWlxEbac_XOq1MOlf9iOKHEsxXspzbjK0vLpy8BwjwII3iRbRXUcDxrhAdkZmFlI15nySCSEZ7g922tF1Xln5DCPEgYYvZ1L4v4rPu_UqLfcHPtwSb2OH2GhPgVcVhhH6DpkQI8CDZCIoR20sC-uchP40oAmcLm9EJFV7xzwplj54AeVadXQjxILvLBjPFpCoz29m9Yf2qRnV7PI9GqxE8ozVQfk9QwCqrCPEgZXcMudvEoB_MJ8tqOW2PLTKAIeQBnE-1bfzptRc2gR8I8VkBAAAAAfXq-bmxWqOz7B5wKkwjzHGv2R4s7Y0Z76LqXWYNhmz0AAAAAAD-____Av0cAAAAAAAAFgAUl-skmdZDtn7Hnub6mF4HP2uVn7oAAAAAAAAAACJqIPAE4MsOAAgI8CBDmQsbEXc46Hu8DivhCBM1LGExa4TTM-wo7HpoCVjBTQgI8CCty5vkQtPHzzs8xqArOYhVSjgaDoG1ou3cojv5_P7wQQgI8SDQWB0kdXCTwbk-TqTt0QfRMyzDNLOtU1XXFgvGSRlW8wgI8CC2PKa_QCIBZtrXodq1GdEzppISMsMRDOnzr2gFjLKOAAgI8CCwQ_QF67bcFk_uJ2s0VCZmf5PGIjTmTCpt_qnVY5p_8AgI8SAbzyx7z-oxPMju6PvtQhzrJIQyH2ZAc9oyLuYemzbmZQgI8CC5bh7J74uUk91r8LwybHQFCNBC3PWeuwtMCCNFKWj19AgI8SAf4R2TUNPjaX_PWDUImpoITK0JoW89zaMKnD1wlEEi8AgI8SC2vNmdm7eyP5Ytl1yTzT0njliMdALl1ViKG-s3bG2zswgI8CCpbIVNz1GFVXdJk2zd82hBUoNFFemUPBt7IJdWEOciPwgI8CBtYdRQcrtX1FtCm1SxF7sx-5cO04U8KzbJh8fqBkyReAgI8CBHs2LGmX6gI-lV7yp1RrV7_tGfdiBAwnEFF6B6yXHzAQgI8CATotVmbXBMAixhZ-QKy5Q4lR0FusdA_wcIC1TbB7GmxAgIAAWIlg1z1xkBA-KXOw"],"envelope":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIY4iYpZLrhVZchEFlTi7Ix_wgrf6yVzuqi2lx7aiGUC3xIGN557LqR6YoCunS1cTEzH_edE75Tn3MO9fmAz1AfPeqCPAgWhSWAlQqXEIvMvwMJdxWvVHsiQVpnbMy2X74ZtIwffMI8CDjbjOl-ux3o7s8RP1xPkN2Lx96Vq0t1wGlkbSzoiDKigjxINmP76YQKWAX3y_usdzY-cH0F_ejQRwIlZlv1tpRFVhXCPAgKb2WiNdzFA-9wChqVq_D5eQo03BRAX8mD_EiouEBWEgI8SCEdAuprEhxQA28-Y-mxpDPnHFYrXFpW_ygfSJlChoA6gjxIDLuS2H5mkQT51okBzSqxvYOZ2DzeEjrKj1FhjpNDRblCPAgOatp97sEGfSkPectTIcXn_UGSclxLvXC9ouOsHYFkl8I8CBPLfD1TsHdjhkyZ9iTm9m5GTCSBT-7GhYUfap1vptsnQjxINBAKCf3cKChW811B6TkfdlxdONUiLQA88uJMnPer4KuCPEgytIBB3x7TFDT-XqOV-9vpqw1NKoAu0dhtsCbAMql2L0I8CCtNZgmApuKULvPC9nsMCaM05arV-F3o5FTlnJCnRvdMgjwIBGYo5Vxy-d7U5zKv5vp3Ii7hJPH_BDLCzA13c47p9q7CP_wCHbghVgOFMuNCPAQPZK2lHbTMqcCYUotzOQcmQjwIJ7ruRIs6HnufKxCpmLUgeUl0aUu0ov4_3PqcppS-bddCPEgI530vHzdwz_3o9jYQ3WablSa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