{"id":139,"date":"2010-08-21T14:04:00","date_gmt":"2010-08-21T12:04:00","guid":{"rendered":"http:\/\/djalil.chafai.net\/blog\/?p=139"},"modified":"2023-05-17T22:36:24","modified_gmt":"2023-05-17T20:36:24","slug":"ludwig-boltzmann-1844-1906","status":"publish","type":"post","link":"https:\/\/djalil.chafai.net\/blog\/2010\/08\/21\/ludwig-boltzmann-1844-1906\/","title":{"rendered":"Ludwig Boltzmann (1844 - 1906)"},"content":{"rendered":"<p style=\"text-align: center;\"><a href=\"\/blog\/wp-content\/uploads\/2010\/08\/Boltzmann.jpg\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-141\" title=\"Ludwig Boltzmann, young\" src=\"\/blog\/wp-content\/uploads\/2010\/08\/Boltzmann.jpg\" alt=\"\" width=\"257\" height=\"326\" srcset=\"https:\/\/djalil.chafai.net\/blog\/wp-content\/uploads\/2010\/08\/Boltzmann.jpg 257w, https:\/\/djalil.chafai.net\/blog\/wp-content\/uploads\/2010\/08\/Boltzmann-236x300.jpg 236w\" sizes=\"(max-width: 257px) 100vw, 257px\" \/><\/a><\/p>\n<p style=\"text-align: justify;\">I traveled to\u00a0 Austria this summer, for vacations. It was impossible to avoid visiting the <a title=\"Zentralfriedhof of Vienna, in Wikipedia\" href=\"http:\/\/en.wikipedia.org\/wiki\/Zentralfriedhof\">Zentralfriedhof of Vienna<\/a>, where one can contemplate the grave of a great viennese scientist: <a title=\"Ludwig Boltzmann, on Wikipedia\" href=\"http:\/\/en.wikipedia.org\/wiki\/Ludwig_Boltzmann\">Ludwig Boltzmann<\/a>. His ideas in mathematical physics were amazingly original, beautiful, and deep.\u00a0 He understood the power of melting probability and partial differential equations before the rigorous developments of these fields in mathematics and physics. His elementary derivation of the entropy formula from the combinatorics of microstates is also striking,\u00a0 years before the formulation of the quantum hypothesis by <a title=\"Max Planck in Wikipedia\" href=\"http:\/\/en.wikipedia.org\/wiki\/Max_Planck\">Max Planck<\/a> and the concept of information by <a title=\"Claude Shannon, in Wikipedia\" href=\"http:\/\/en.wikipedia.org\/wiki\/Claude_Shannon\">Claude Shannon<\/a>. Unfortunately, his ideas were not well received at that time, and he eventually committed suicide in Italy after a severe depression. Nevertheless, his work had an enormous impact on science. In 2010, <a title=\"C\u00e9dric Villani in Wikipedia\" href=\"http:\/\/en.wikipedia.org\/wiki\/C%C3%A9dric_Villani\">C\u00e9dric Villani<\/a> received a Fields Medal partly for his study of the Boltzmann equation of kinetic theory of gases. You may take a look at <a title=\"Cercignani's conjecture is sometimes true and always almost true\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=1964379\">his paper on the Cercignani conjecture<\/a> and the more recent paper by <a title=\"Celebrating Cercignani's conjecture for the Boltzmann equation\" href=\"http:\/\/arxiv.org\/abs\/1009.4006\">Desvillettes, Mouhot, and Villani<\/a>.<\/p>\n<p style=\"text-align: justify;\">In the nineteenth century, probability theory was not yet developed, and stochastic models were called <em>statistical models<\/em>. This is why we say <em>statistical mechanics<\/em> and <em>statistical physics<\/em>.\u00a0 You may take a look at the <a title=\"The conceptual foundations of the statistical approach in mechanics\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=1106634\">pretty interesting small old book by Paul and Tatiana Ehrenfest<\/a>.<\/p>\n<p style=\"text-align: justify;\"><a title=\"Ludwig Boltzmann, on Wikipedia\" href=\"http:\/\/en.wikipedia.org\/wiki\/Ludwig_Boltzmann\"><img loading=\"lazy\" class=\"size-full wp-image-140  aligncenter\" title=\"Entropy formula, Boltzmann grave stone, Zentralfriedhof, Vienna\" src=\"\/blog\/wp-content\/uploads\/2010\/08\/entropy.jpg\" alt=\"\" width=\"320\" height=\"90\" srcset=\"https:\/\/djalil.chafai.net\/blog\/wp-content\/uploads\/2010\/08\/entropy.jpg 320w, https:\/\/djalil.chafai.net\/blog\/wp-content\/uploads\/2010\/08\/entropy-300x84.jpg 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>I traveled to&nbsp; Austria this summer, for vacations. It was impossible to avoid visiting the Zentralfriedhof of Vienna, where one can contemplate the grave of&#8230;<\/p>\n<div class=\"more-link-wrapper\"><a class=\"more-link\" href=\"https:\/\/djalil.chafai.net\/blog\/2010\/08\/21\/ludwig-boltzmann-1844-1906\/\">Continue reading<span class=\"screen-reader-text\">Ludwig Boltzmann (1844 - 1906)<\/span><\/a><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":253},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts\/139"}],"collection":[{"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/comments?post=139"}],"version-history":[{"count":42,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts\/139\/revisions"}],"predecessor-version":[{"id":17786,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts\/139\/revisions\/17786"}],"wp:attachment":[{"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/media?parent=139"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/categories?post=139"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/tags?post=139"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}