{"id":10567,"date":"2025-08-18T09:10:55","date_gmt":"2025-08-18T00:10:55","guid":{"rendered":"https:\/\/unit.nifs.ac.jp\/research\/?post_type=report&#038;p=10567"},"modified":"2025-08-18T09:14:31","modified_gmt":"2025-08-18T00:14:31","slug":"report-10558_en","status":"publish","type":"report","link":"https:\/\/unit.nifs.ac.jp\/research\/archives\/report\/report-10558_en","title":{"rendered":"Landau Damping, Schr\u00f6dinger Equation, and Fluctuation Theorem"},"content":{"rendered":"\n<p>Hideo Sugama summarized his research as \u201cLinear Landau damping, Schr\u00f6dinger equation, and fluctuation theorem,\u201d and his paper has been published Physics of Plasmas.<\/p>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>\u3010Abstract\u3011<br>Landau damping has long been studied as one of the principal physical mechanisms responsible not only for wave heating observed in high-temperature plasmas in space and in fusion devices, but also for stabilizing microinstabilities and geodesic acoustic modes (GAMs). Landau damping is a seemingly irreversible process despite occurring in collisionless plasmas governed by the Vlasov equation, which possesses time-reversal symmetry. On the other hand, the fluctuation theorem, derived from reversible dynamics, states that the probability ratio of entropy production to entropy reduction increases exponentially with time, thereby providing a microscopic foundation for the second law of thermodynamics and nonequilibrium statistical mechanics. In this study, the linear Vlasov\u2013Poisson system is reformulated in the form of the Schr\u00f6dinger equation, so that time-reversal symmetry and conservation laws can be expressed concisely. This formulation shows that the fluctuation theorem holds for the relative stochasitc entropy, defined from the probability density functional of the particle velocity distribution function. The difference between the energy perturbation normalized by the equilibrium temperature and the entropy pertubation constitutes a time-independent invariant of the system. This invariant is a quadratic form of the perturbed component of the velocity distribution function and corresponds to the squared amplitude of the state vector that satisfies the Schr\u00f6dinger equation. Furthermore, the eigenvectors of the Hamiltonian corresponding to Case\u2013Van Kampen modes are derived. By constructing exact solutions from these eigenvectors and employing them, the fluctuation theorem for the Landau damping process is formulated and its validity is verified through numerical simulations. These results provide a new formulation of collisionless plasma physical processes from the perspective of nonequilibrium statistical mechanics.<\/p>\n\n\n\n<div style=\"height:16px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"480\" src=\"http:\/\/unit.nifs.ac.jp\/research\/wp-content\/uploads\/2025\/08\/Sugama2508Fig.jpg\" alt=\"\" class=\"wp-image-10559\" style=\"width:640px\" srcset=\"https:\/\/unit.nifs.ac.jp\/research\/wp-content\/uploads\/2025\/08\/Sugama2508Fig.jpg 1024w, https:\/\/unit.nifs.ac.jp\/research\/wp-content\/uploads\/2025\/08\/Sugama2508Fig-300x141.jpg 300w, https:\/\/unit.nifs.ac.jp\/research\/wp-content\/uploads\/2025\/08\/Sugama2508Fig-768x360.jpg 768w, https:\/\/unit.nifs.ac.jp\/research\/wp-content\/uploads\/2025\/08\/Sugama2508Fig-180x84.jpg 180w, https:\/\/unit.nifs.ac.jp\/research\/wp-content\/uploads\/2025\/08\/Sugama2508Fig-500x234.jpg 500w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Figure: <br>(a) Probability density function <em>P(\u2206S)<\/em> of the stochastic relative entropy, and<br>(b) ratio <em>P(\u2206S)\/P(\u2212\u2206S)<\/em> of the probabilities of entropy increase to decrease, obtained from numerical simulations.<\/figcaption><\/figure>\n<\/div>\n\n\n<div style=\"height:24px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>\u3010Publications\u3011<\/p>\n\n\n\n<p><a href=\"https:\/\/doi.org\/10.1063\/5.0284500\" target=\"_blank\" rel=\"noreferrer noopener\">H. Sugama, &#8220;Linear Landau damping, Schr\u00f6dinger equation, and fluctuation theorem&#8221;, Phys. Plasmas Vol.32, 080701 (2025).<br>https:\/\/doi.org\/10.1063\/5.0284500<\/a><\/p>\n\n\n\n<p><\/p>\n","protected":false},"author":9,"featured_media":10559,"menu_order":0,"template":"","meta":{"_acf_changed":false,"footnotes":""},"ppma_author":[347],"class_list":["post-10567","report","type-report","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/unit.nifs.ac.jp\/research\/wp-json\/wp\/v2\/report\/10567","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/unit.nifs.ac.jp\/research\/wp-json\/wp\/v2\/report"}],"about":[{"href":"https:\/\/unit.nifs.ac.jp\/research\/wp-json\/wp\/v2\/types\/report"}],"author":[{"embeddable":true,"href":"https:\/\/unit.nifs.ac.jp\/research\/wp-json\/wp\/v2\/users\/9"}],"version-history":[{"count":2,"href":"https:\/\/unit.nifs.ac.jp\/research\/wp-json\/wp\/v2\/report\/10567\/revisions"}],"predecessor-version":[{"id":10573,"href":"https:\/\/unit.nifs.ac.jp\/research\/wp-json\/wp\/v2\/report\/10567\/revisions\/10573"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/unit.nifs.ac.jp\/research\/wp-json\/wp\/v2\/media\/10559"}],"wp:attachment":[{"href":"https:\/\/unit.nifs.ac.jp\/research\/wp-json\/wp\/v2\/media?parent=10567"}],"wp:term":[{"taxonomy":"author","embeddable":true,"href":"https:\/\/unit.nifs.ac.jp\/research\/wp-json\/wp\/v2\/ppma_author?post=10567"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}