{"id":69,"date":"2016-02-16T14:32:55","date_gmt":"2016-02-16T14:32:55","guid":{"rendered":"http:\/\/bifi.es\/~acastro\/?p=69"},"modified":"2016-02-17T18:42:33","modified_gmt":"2016-02-17T18:42:33","slug":"nonextensive-thermodynamic-fun-ctions-in-the-schrodinger-gibbs-ensemble","status":"publish","type":"post","link":"https:\/\/personal.unizar.es\/acastro\/?p=69","title":{"rendered":"Nonextensive thermodynamic functions in the Schr\u00f6dinger-Gibbs ensemble"},"content":{"rendered":"<p>J. L. Alonso, A. Castro, J. Clemente-Gallardo, J. C. Cuch \u0301\u0131, P. Echenique, J. G. Esteve, and F. Falceto,\u00a0<a href=\"http:\/\/dx.doi.org\/10.1103\/PhysRevE.91.022137\" target=\"_blank\">Phys. Rev. E <strong>91<\/strong>, 022137\u00a0(2015)<\/a>.<\/p>\n<p>Schr\u00f6dinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that\u00a0quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only\u00a0allowed states for a quantum system [E. Schr\u00f6dinger, Statistical Thermodynamics (Courier Dover, Mineola,\u00a01967)]. Different authors have interpreted this statement by introducing density distributions on the space of\u00a0quantum pure states with weights obtained as functions of the expectation value of the Hamiltonian of the\u00a0system. In this work we focus on one of the best known of these distributions and prove that, when considered in\u00a0composite quantum systems, it defines partition functions that do not factorize as products of partition functions\u00a0of the noninteracting subsystems, even in the thermodynamical regime. This implies that it is not possible to\u00a0define extensive thermodynamical magnitudes such as the free energy, the internal energy, or the thermodynamic\u00a0entropy by using these models. Therefore, we conclude that this distribution inspired by Schr\u00f6dinger\u2019s idea\u00a0cannot be used to construct an appropriate quantum equilibrium thermodynamics.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>J. L. Alonso, A. Castro, J. Clemente-Gallardo, J. C. Cuch \u0301\u0131, P. Echenique, J. G. Esteve, and F. Falceto,\u00a0Phys. Rev. E 91, 022137\u00a0(2015). Schr\u00f6dinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that\u00a0quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only\u00a0allowed states for a quantum system [E. Schr\u00f6dinger, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-69","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=\/wp\/v2\/posts\/69"}],"collection":[{"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=69"}],"version-history":[{"count":4,"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=\/wp\/v2\/posts\/69\/revisions"}],"predecessor-version":[{"id":89,"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=\/wp\/v2\/posts\/69\/revisions\/89"}],"wp:attachment":[{"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=69"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=69"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/personal.unizar.es\/acastro\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=69"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}