{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T22:58:40Z","timestamp":1790722720147,"version":"4.1.0"},"reference-count":50,"publisher":"American Physical Society (APS)","issue":"16","license":[{"start":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T00:00:00Z","timestamp":1760486400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000761","name":"Imperial College London","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000761","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. Lett."],"accepted":{"date-parts":[[2025,9,10]]},"abstract":"<jats:p>\n                    Stochastic resetting breaks detailed balance and drives the formation of nonequilibrium steady states. Here, we consider a chain of diffusive processes\n                    <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <a:mrow>\n                        <a:msub>\n                          <a:mrow>\n                            <a:mi>x<\/a:mi>\n                          <\/a:mrow>\n                          <a:mrow>\n                            <a:mi>i<\/a:mi>\n                          <\/a:mrow>\n                        <\/a:msub>\n                        <a:mo stretchy=\"false\">(<\/a:mo>\n                        <a:mi>t<\/a:mi>\n                        <a:mo stretchy=\"false\">)<\/a:mo>\n                      <\/a:mrow>\n                    <\/a:math>\n                    that interact unilaterally: at random time intervals, the process\n                    <e:math xmlns:e=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <e:msub>\n                        <e:mi>x<\/e:mi>\n                        <e:mi>n<\/e:mi>\n                      <\/e:msub>\n                    <\/e:math>\n                    stochastically resets to the instantaneous value of\n                    <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <g:msub>\n                        <g:mi>x<\/g:mi>\n                        <g:mrow>\n                          <g:mi>n<\/g:mi>\n                          <g:mo>\u2212<\/g:mo>\n                          <g:mn>1<\/g:mn>\n                        <\/g:mrow>\n                      <\/g:msub>\n                    <\/g:math>\n                    . We derive analytically the steady-state statistics of these nested stochastic resetting processes including the stationary distribution for each process as well as its moments. We are also able to calculate exactly the steady-state two-point correlations\n                    <i:math xmlns:i=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <i:mo stretchy=\"false\">\u27e8<\/i:mo>\n                      <i:msub>\n                        <i:mi>x<\/i:mi>\n                        <i:mi>n<\/i:mi>\n                      <\/i:msub>\n                      <i:msub>\n                        <i:mi>x<\/i:mi>\n                        <i:mrow>\n                          <i:mi>n<\/i:mi>\n                          <i:mo>+<\/i:mo>\n                          <i:mi>j<\/i:mi>\n                        <\/i:mrow>\n                      <\/i:msub>\n                      <i:mo stretchy=\"false\">\u27e9<\/i:mo>\n                    <\/i:math>\n                    between processes by mapping the problem to one of the ordering statistics of random counting processes. Understanding statistics and correlations in many-particle nonequilibrium systems remains a formidable challenge and our results provide an example of such tractable correlations. We expect this framework will both help build a model-independent framework for random processes with unilateral interactions and find immediate applications, e.g., in the modeling of lossy information propagation.\n                  <\/jats:p>","DOI":"10.1103\/ccjj-6ksn","type":"journal-article","created":{"date-parts":[[2025,9,10]],"date-time":"2025-09-10T14:51:01Z","timestamp":1757515861000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Nested Stochastic Resetting: Nonequilibrium Steady States and Exact Correlations"],"prefix":"10.1103","volume":"135","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6636-6350","authenticated-orcid":true,"given":"Henry","family":"Alston","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/041kmwe10","id-type":"ROR","asserted-by":"publisher"}],"name":"Imperial College London"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-4456-3323","authenticated-orcid":true,"given":"Callum","family":"Britton","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/041kmwe10","id-type":"ROR","asserted-by":"publisher"}],"name":"Imperial College London"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9812-7904","authenticated-orcid":true,"given":"Thibault","family":"Bertrand","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/041kmwe10","id-type":"ROR","asserted-by":"publisher"}],"name":"Imperial College London"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2025,10,15]]},"reference":[{"key":"ccjj-6ksnCc1R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.106.160601","type":"journal-article"},{"key":"ccjj-6ksnCc2R1","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ab7cfe","type":"journal-article"},{"key":"ccjj-6ksnCc3R1","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/44\/43\/435001","type":"journal-article"},{"key":"ccjj-6ksnCc4R1","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/18\/3\/033006","type":"journal-article"},{"key":"ccjj-6ksnCc5R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.93.022106","type":"journal-article"},{"key":"ccjj-6ksnCc6R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.108.014112","type":"journal-article"},{"key":"ccjj-6ksnCc7R1","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ad62c9","type":"journal-article"},{"key":"ccjj-6ksnCc8R1","doi-asserted-by":"publisher","DOI":"10.1038\/nature06201","type":"journal-article"},{"key":"ccjj-6ksnCc9R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.94.198101","type":"journal-article"},{"key":"ccjj-6ksnCc10R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.103.022135","type":"journal-article"},{"key":"ccjj-6ksnCc11R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.128.200603","type":"journal-article"},{"key":"ccjj-6ksnCc12R1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511606014","type":"book","volume-title":"A Guide to First-Passage Processes","author":"S. 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All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2025","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92025 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"167101"}}