{"id":122641,"date":"2015-09-08T02:00:00","date_gmt":"2015-09-07T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=bef0ea9111681cd458371906d8a55228"},"modified":"2015-09-08T02:00:00","modified_gmt":"2015-09-07T23:00:00","slug":"equivalent-norms-in-img-httpej-iop-orgimages0143-0807366065021toc_ejp518814ieqn1-gifmathbbrn-from-thermodynamical-laws","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=122641","title":{"rendered":"Equivalent norms in ##IMG## [http:\/\/ej.iop.org\/images\/0143-0807\/36\/6\/065021\/toc_ejp518814ieqn1.gif]\r\n{${{mathbb{R}}}^{n}$} from thermodynamical laws"},"content":{"rendered":"<p>In 1978, Landsberg proposed an elegant way of obtaining the inequality between arithmetic and<br \/>\ngeometric mean by using the first and second laws of thermodynamics. This result opened a debate on<br \/>\nthe logic legitimacy of this procedure to obtain some mathematical truths. Although this discussion<br \/>\ncan not be considered completed, the Landsberg approach has shown a great richness in obtaining many<br \/>\nalgebraic inequalities. In the present article we apply the Landsberg method to some properties of<br \/>\nnormed spaces trough a vector space of temperatures. In this way, the result that establishes the<br \/>\nequivalence between all p -norms in the space ##IMG##<br \/>\n[http:\/\/ej.iop.org\/images\/0143-0807\/36\/6\/065021\/ejp518814ieqn3.gif] {${{mathbb{R}}}^{n}$} and the<br \/>\nminimal constant that guaranties this fact are readily found. Geometrical surfaces stemming from<br \/>\nenergy conservation are a consequence of this interpretation. In this manner, an application for<br \/>\nthermal equilibrium of n&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In 1978, Landsberg proposed an elegant way of obtaining the inequality between arithmetic and<br \/>\ngeometric mean by using the first and second laws of thermodynamics. This result opened a debate on<br \/>\nthe logic legitimacy of this procedure to obtain some ma&#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-122641","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\/122641","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=122641"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/122641\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=122641"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=122641"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=122641"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}