论文标题
熵，从克劳西乌斯到功能不平等
The entropy, from Clausius to functional inequalities
论文作者
论文摘要
在本文档中，我们对熵感兴趣。熵是多重的，其想法是描述物理学家克劳西乌斯提出的定义。确实，克劳西乌斯（Clausius）在1865年暴露了热力学的第二个原理，也提出了熵的概念。它实际上将定义一个足够通用的概念，可以在数学的许多领域中使用。从1865年克劳西乌斯（Clausius）的定义开始，我将尝试解释基本的功能不平等，例如Sobolev不平等，分析的关键点，自然而然地用特定的熵墨。这条路径使我能够概述在有限或无限维度，巴克里 - 美食理论以及最近的奥托演算中使用梯度流的使用。
In this document we are interested in entropy. Entropy is multiple, the idea is to describe the definition proposed by the physicist Clausius. Indeed, Clausius exposes in 1865 the second principle of thermodynamics and also proposes the concept of entropy. Instead of simply defining a functional, central point for the development of the second principle, it will in fact define a concept sufficiently general to be used in many fields of mathematics.In these few pages, I wish to show the role played by entropy in the field of gradient flows and functional inequalities. Starting from the definition of Clausius in 1865, I will try to explain how fundamental functional inequalities like Sobolev inequality, key point in analysis, are natural inked with a particular entropy. This path allows me to give an overview of the use of gradient flows in finite or infinite dimension, of Bakry-Emery theory and more recently of Otto's calculus.
