{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T11:32:54Z","timestamp":1769772774759,"version":"3.49.0"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T00:00:00Z","timestamp":1767571200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T00:00:00Z","timestamp":1767571200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Stat Phys"],"DOI":"10.1007\/s10955-025-03558-y","type":"journal-article","created":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T14:41:51Z","timestamp":1767624111000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hydrodynamic Limit for Some Gradient and Attractive Spin Models"],"prefix":"10.1007","volume":"193","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0616-1481","authenticated-orcid":false,"given":"Chiara","family":"Franceschini","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8093-8810","authenticated-orcid":false,"given":"Patr\u00edcia","family":"Gon\u00e7alves","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2237-0032","authenticated-orcid":false,"given":"Kohei","family":"Hayashi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4184-108X","authenticated-orcid":false,"given":"Makiko","family":"Sasada","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,1,5]]},"reference":[{"key":"3558_CR1","unstructured":"Billingsley, P.: Convergence of probability measures. John Wiley & Sons, (2013)"},{"issue":"2","key":"3558_CR2","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s10955-024-03240-9","volume":"191","author":"M Capanna","year":"2024","unstructured":"Capanna, M., Gabrielli, D., Tsagkarogiannis, D.: On a class of solvable stationary non equilibrium states for mass exchange models. J. Stat. Phys. 191(2), 25 (2024)","journal-title":"J. Stat. Phys."},{"key":"3558_CR3","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1007\/s10955-013-0786-9","volume":"152","author":"G Carinci","year":"2013","unstructured":"Carinci, G., Giardin\u00e0, C., Giberti, C., Redig, F.: Duality for stochastic models of transport. J. Stat. Phys. 152, 657\u2013697 (2013)","journal-title":"J. Stat. Phys."},{"issue":"60","key":"3558_CR4","first-page":"1","volume":"21","author":"L Fajfrov\u00e1","year":"2016","unstructured":"Fajfrov\u00e1, L., Gobron, T., Saada, E.: Invariant measures of mass migration processes. Electron. J. Probab. 21(60), 1\u201352 (2016)","journal-title":"Electron. J. Probab."},{"issue":"2","key":"3558_CR5","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/S0304-4149(96)00121-4","volume":"66","author":"S Feng","year":"1997","unstructured":"Feng, S., Iscoe, I., Sepp\u00e4l\u00e4inen, T.: A microscopic mechanism for the porous medium equation. Stochastic Processes and their Applications 66(2), 147\u2013182 (1997)","journal-title":"Stochastic Processes and their Applications"},{"key":"3558_CR6","doi-asserted-by":"crossref","unstructured":"Franceschini, C., Frassek, R., Giardin\u00e0, C.: Integrable heat conduction model. Journal of Mathematical Physics, 64(4), (2023)","DOI":"10.1063\/5.0138013"},{"issue":"2","key":"3558_CR7","doi-asserted-by":"publisher","first-page":"1340","DOI":"10.3150\/21-BEJ1390","volume":"28","author":"C Franceschini","year":"2022","unstructured":"Franceschini, C., Gon\u00e7alves, P., Sau, F.: Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. Bernoulli 28(2), 1340\u20131381 (2022)","journal-title":"Bernoulli"},{"issue":"1","key":"3558_CR8","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/s10955-019-02375-4","volume":"180","author":"R Frassek","year":"2020","unstructured":"Frassek, R., Giardin\u00e0, C., Kurchan, J.: Non-compact quantum spin chains as integrable stochastic particle processes. J. Stat. Phys. 180(1), 135\u2013171 (2020)","journal-title":"J. Stat. Phys."},{"key":"3558_CR9","doi-asserted-by":"crossref","unstructured":"Giardin\u00e0, C., Redig, F.: Duality for Markov processes: a Lie-algebraic approach. In preparation, (2025)","DOI":"10.1007\/978-3-032-04099-2"},{"issue":"4","key":"3558_CR10","first-page":"1132","volume":"46","author":"T Gobron","year":"2010","unstructured":"Gobron, T., Saada, E.: Couplings, attractiveness and hydrodynamics for conservative particle systems. Annales de l\u2019IHP Probabilit\u00e9s et statistiques 46(4), 1132\u20131177 (2010)","journal-title":"Annales de l\u2019IHP Probabilit\u00e9s et statistiques"},{"key":"3558_CR11","unstructured":"Kim, S., Quattropani, M., Sau, F.: Spectral gap of the KMP and other stochastic exchange models on arbitrary graphs. arXiv preprint arXiv:2505.02400, (2025)"},{"key":"3558_CR12","doi-asserted-by":"crossref","unstructured":"Kipnis, C., Landim, C.: Scaling limits of interacting particle systems, volume 320. Springer Science & Business Media, (1999)","DOI":"10.1007\/978-3-662-03752-2"},{"key":"3558_CR13","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/BF01011740","volume":"27","author":"C Kipnis","year":"1982","unstructured":"Kipnis, C., Marchioro, C., Presutti, E.: Heat flow in an exactly solvable model. J. Stat. Phys. 27, 65\u201374 (1982)","journal-title":"J. Stat. Phys."},{"key":"3558_CR14","doi-asserted-by":"crossref","unstructured":"Liggett, T.\u00a0M.: Interacting particle systems. Springer, (1985)","DOI":"10.1007\/978-1-4613-8542-4"},{"key":"3558_CR15","first-page":"596","volume":"59","author":"L Lipatov","year":"1994","unstructured":"Lipatov, L.: High energy asymptotics of multi-colour QCD and exactly solvable lattice models. J. Exp. Theor. Phys. Lett. 59, 596\u2013599 (1994)","journal-title":"J. Exp. Theor. Phys. Lett."},{"issue":"3","key":"3558_CR16","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1007\/BF02099130","volume":"140","author":"F Rezakhanlou","year":"1991","unstructured":"Rezakhanlou, F.: Hydrodynamic limit for attractive particle systems on $$\\mathbb{Z} ^d$$. Commun. Math. Phys. 140(3), 417\u2013448 (1991)","journal-title":"Commun. Math. Phys."},{"key":"3558_CR17","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/BF01197337","volume":"95","author":"Y Suzuki","year":"1993","unstructured":"Suzuki, Y., Uchiyama, K.: Hydrodynamic limit for a spin system on a multidimensional lattice. Probab. Theory Relat. Fields 95, 47\u201374 (1993)","journal-title":"Probab. Theory Relat. Fields"}],"container-title":["Journal of Statistical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10955-025-03558-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10955-025-03558-y","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10955-025-03558-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T09:49:26Z","timestamp":1769680166000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10955-025-03558-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,5]]},"references-count":17,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["3558"],"URL":"https:\/\/doi.org\/10.1007\/s10955-025-03558-y","relation":{},"ISSN":["1572-9613"],"issn-type":[{"value":"1572-9613","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,5]]},"assertion":[{"value":"16 May 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 December 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 January 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of Interest"}}],"article-number":"3"}}