2025 SES G.I. Taylor Medal Plenary Lecture

Rational Extended Thermodynamics: A Bridge between Mesoscopic and Macroscopic Scales

In many physical systems, phenomena occur across multiple scales—microscopic, mesoscopic, and macroscopic. A compelling mathematical challenge, closely related to the unsolved Sixth Hilbert Problem, is to rigorously establish connections between these scales. In this talk, we present a brief history of Rational Extended Thermodynamics (RET), a theory that bridges mesoscopic and macroscopic descriptions. We begin with early approaches based on the closure of the moment hierarchy in the Boltzmann equation for monatomic rarefied gases and progress to recent developments for polyatomic and dense gases, gas mixtures, and new formulations addressing viscoelastic behavior. RET is grounded in the universal principles of continuum mechanics, with particular emphasis on the compatibility of general hyperbolic systems with the entropy law governed by a convex entropy function. From a mathematical standpoint, the resulting system of partial differential equations is shown to be symmetric hyperbolic, ensuring the well-posedness of the Cauchy problem and favorable qualitative properties. Experimental results on sound wave propagation, shock waves in polyatomic gases, and stress decay in viscoelastic materials are compared with the theoretical predictions of RET.

Bio of the speaker: Tommaso Ruggeri is an Italian mathematical physicist and Emeritus Professor at the University of Bologna. He is the author of over 300 scientific publications and several influential books and is internationally recognized for his work in nonlinear wave propagation, hyperbolic systems with convex entropy, and classical and relativistic continuum mechanics. He is one of the founders of modern Rational Extended Thermodynamics, a theory connecting continuum and kinetic descriptions. Together with Ingo Müller, he co-authored the well-known book Rational Extended Thermodynamics, which has become a standard reference in the field. His recent books, written in collaboration with Masaru Sugiyama, extend this theory to polyatomic gases, gas mixtures, and relativistic regimes. In mathematical relativity, he collaborated with Yvonne Choquet-Bruhat to prove that the 3+1 decomposition of Einstein’s vacuum field equations is strictly hyperbolic under appropriate conditions, establishing the well-posedness of the initial value problem in general relativity. He is a member of several prestigious academies, including the Accademia Nazionale dei Lincei, Academia Europaea, the European Academy of Sciences and Arts, and EurASc, and has received several prizes. He has served as Director of the National Group of Mathematical Physics and as President of the Scientific Committee of the Istituto Nazionale di Alta Matematica. He has been invited as a plenary speaker and visiting professor at leading institutions worldwide, including Stanford, Brown, Paris, Berlin, Seoul, Taipei, Mumbai, Hong Kong, Sydney, Kyoto, and Beijing. He also serves as an associate editor of several international journals and has mentored numerous students who are now professors.