标题： 热力学 of $f(R)$ 理论 显示英文标题

标题： Thermodynamics of $f(R)$ Theories

摘要： 这一系列三场讲座是在“Escola de Cosmologia e Gravitação”\url{https://cosmosecontexto.org.br/ecg-inscricoes}举办的，并在\url{https://shorturl.at/2ZSI7}进行了网络直播——用葡萄牙语，但幻灯片是英文的。 我们将简要回顾$f(R)$理论（在度规方法中）以及成功修改广义相对论的一般要求。 然后我们将展开一个大的括号，讨论一种非标准的相变方法：突变理论。 最后，我们将把前面的讲座联系起来，介绍对$f(R)$理论的一种新的热力学解释。 显示英文摘要

摘要： This series of three lectures was presented at ``Escola de Cosmologia e Gravita\c{c}\~ao" \url{https://cosmosecontexto.org.br/ecg-inscricoes} and webcast at \url{https://shorturl.at/2ZSI7} -- in Portuguese, but slides in English. We will go through a brief review on $f(R)$ theories (in the metric approach) and the usual requirements for successful modifications of General Relativity. Then we will open a large parenthesis to talk about a non-standard approach to Phase Transitions: the Catastrophe Theory. Finally, we will connect the previous lectures to introduce a new Thermodynamic interpretation of $f(R)$ theories.