Geometry, Information and Thermodynamics

Abstract: The geometric formulation of thermodynamics has a long history, from Gibbs to Carathéodory to the more recent developments in contact and information geometry. In this talk I will give a panoramic view of the latter, focusing on how differential geometry provides a natural language for understanding equilibrium and non‑equilibrium phenomena. I will begin by introducing the structures underlying information geometry, presenting several recent results along the way. The talk will be self‑contained and aims to show how geometry offers a unified framework to study thermodynamics, stochastic dynamics, and information theory.