{"id":520179,"date":"2017-09-26T02:00:00","date_gmt":"2017-09-25T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=1d85016032880acec527cfd16504c984"},"modified":"2017-09-26T02:00:00","modified_gmt":"2017-09-25T23:00:00","slug":"statistical-mechanics-of-few-particle-systems-exact-results-for-two-useful-models","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=520179","title":{"rendered":"Statistical mechanics of few-particle systems: exact results for two useful models"},"content":{"rendered":"<p>The statistical mechanics of small clusters ( n\u00a0\u223c\u00a010\u201350 elements) of harmonic oscillators and<br \/>\ntwo-level systems is studied exactly, following the microcanonical, canonical and grand canonical<br \/>\nformalisms. For clusters with several hundred particles, the results from the three formalisms<br \/>\ncoincide with those found in the thermodynamic limit. However, for clusters formed by a few tens of<br \/>\nelements, the three ensembles yield different results. For a cluster with a few tens of harmonic<br \/>\noscillators, when the heat capacity per oscillator is evaluated within the canonical formalism, it<br \/>\nreaches a limit value equal to k B , as in the thermodynamic case, while within the microcanonical<br \/>\nformalism the limit value is k B (1 \u2013 1\/ n ). This difference could be measured experimentally. For<br \/>\na cluster with a few tens of two-level systems, the heat capacity evaluated within the canonical and<br \/>\nmicrocanonical ensembles also presents dif&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The statistical mechanics of small clusters ( n\u00a0\u223c\u00a010\u201350 elements) of harmonic oscillators and<br \/>\ntwo-level systems is studied exactly, following the microcanonical, canonical and grand canonical<br \/>\nformalisms. For clusters with several hundred partic&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-520179","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/520179","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=520179"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/520179\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=520179"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=520179"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=520179"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}