{"id":1017,"date":"2017-05-31T22:34:46","date_gmt":"2017-05-31T22:34:46","guid":{"rendered":"http:\/\/physics-complex-systems.fr\/?p=1017"},"modified":"2022-03-11T12:57:29","modified_gmt":"2022-03-11T12:57:29","slug":"nonequilibrium-and-active-systems","status":"publish","type":"post","link":"https:\/\/physics-complex-systems.fr\/en\/nonequilibrium-and-active-systems.html","title":{"rendered":"Nonequilibrium and active systems"},"content":{"rendered":"<p>[vc_row][vc_column css=&#8221;.vc_custom_1496399944725{margin-top: -40px !important;margin-bottom: -20px !important;}&#8221;][vc_separator][\/vc_column][\/vc_row][vc_row equal_height=&#8221;yes&#8221;][vc_column width=&#8221;1\/2&#8243;][vc_column_text]<\/p>\n<div style=\"text-align: justify; text-justify: inter-word; color: #363131;\">Statistical mechanics has brought a fundamental change of paradigm in physics: rather than solving complex dynamics (e.g. Newton or Schroedinger equations), the study of matter can now be done using static, probabilistic approaches, provided the system under study is in (thermal) equilibrium. As statistical mechanics progresses towards new area of research (biophysics, geophysics, driven systems), new frameworks are needed to reproduce the successes of equilibrium statistical mechanics. In these lectures, we will study the new tools which have been developed over the past few decades to study non-equilibrium systems.<\/div>\n<div style=\"text-align: justify; text-justify: inter-word; color: #363131;\">The first part of the lectures will be dedicated to study these tools in the context of relaxations towards thermal equilibrium (derivation of Langevin equation, Ito calculus, Fokker-Planck equation &amp; operator, Master equation). In the second part, we will illustrate and apply these tools to study a research field which has attracted a lot of interest recently: active matter. This field encompasses systems in which individual units are able, at the microscopic scale, to convert energy stored in the environment to self-propel (bacteria, active colloids, vibrated granular media, etc.).<\/div>\n<div><\/div>\n<div><strong>Bibliography<\/strong><\/div>\n<ul>\n<li><em>The Fokker-Planck Equation<\/em>. H. Risken, Springer<\/li>\n<li><em>Stochastic Methods &#8211; A Handbook for the Natural and Social Sciences<\/em>, C. Gardiner, Springer.<\/li>\n<li><em>Stochastic Processes in Physics and Chemistry<\/em>, N. van Kampen, Elsevier.<\/li>\n<\/ul>\n<p>[\/vc_column_text][\/vc_column][vc_column width=&#8221;1\/2&#8243; css=&#8221;.vc_custom_1496700346657{background-color: #f7f7f7 !important;}&#8221;][vc_single_image image=&#8221;1502&#8243; img_size=&#8221;full&#8221;][\/vc_column][\/vc_row][vc_row][vc_column width=&#8221;1\/2&#8243;][vc_column_text]<img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1141 alignleft\" src=\"https:\/\/physics-complex-systems.fr\/wp-content\/uploads\/2017\/06\/Van_Wijland.jpg\" alt=\"\" width=\"116\" height=\"120\" \/>Fr\u00e9d\u00e9ric van Wijland<br \/>\n(Universit\u00e9 Paris Cit\u00e9)[\/vc_column_text][\/vc_column][vc_column width=&#8221;1\/2&#8243;][\/vc_column][\/vc_row][vc_row css=&#8221;.vc_custom_1496824111579{margin-top: 20px !important;}&#8221;][vc_column][vc_column_text]<\/p>\n<div class=\"displaytags\" style=\"color: #363131;\">Keywords: <span class=\"etiquette-key\">active matter<\/span> <span class=\"etiquette-key\">bacteria<\/span> <span class=\"etiquette-key\">Ito calculous<\/span> <span class=\"etiquette-key\">Langevin equation<\/span> <span class=\"etiquette-key\">master equation<\/span> <span class=\"etiquette-key\">non-equilibrium dynamics<\/span> <span class=\"etiquette-key\">self-propelled colloids<\/span> <span class=\"etiquette-key\">thermal ratchets<\/span><\/div>\n<p>[\/vc_column_text][\/vc_column][\/vc_row]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[vc_row][vc_column css=&#8221;.vc_custom_1496399944725{margin-top: -40px !important;margin-bottom: -20px !important;}&#8221;][vc_separator][\/vc_column][\/vc_row][vc_row equal_height=&#8221;yes&#8221;][vc_column width=&#8221;1\/2&#8243;][vc_column_text] Statistical mechanics has brought a fundamental change of paradigm in physics: rather than solving complex dynamics (e.g&#8230;.<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[36,11,10],"tags":[115,116,118,23,21,114,117,119],"translation":{"provider":"WPGlobus","version":"2.12.2","language":"en","enabled_languages":["fr","en"],"languages":{"fr":{"title":true,"content":true,"excerpt":false},"en":{"title":false,"content":false,"excerpt":false}}},"_links":{"self":[{"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/posts\/1017"}],"collection":[{"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/comments?post=1017"}],"version-history":[{"count":18,"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/posts\/1017\/revisions"}],"predecessor-version":[{"id":5748,"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/posts\/1017\/revisions\/5748"}],"wp:attachment":[{"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/media?parent=1017"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/categories?post=1017"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physics-complex-systems.fr\/en\/wp-json\/wp\/v2\/tags?post=1017"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}