Dissipation & Power in Physics and Biology: Optimal Mass Transport meets Stochastic Thermodynamics

ABSTRACT
The discovery in 1998 of a link between the Wasserstein-2 metric, entropy, and the heat equation, by Jordan, Kinderlehrer, and Otto, precipitated an increasing relevance of optimal mass transport in the developing subject of nonequilibrium finite-time thermodynamics. Dissipation in finite-time thermodynamic transitions for Langevin models of colloidal particles proved equivalent to the length of trajectories traversed in a suitably metrized manifold of thermodynamic states. This enabling new insight, has led to quantitative bounds on power and efficiency of thermodynamic cycles that supersede classical quasi-static Carnot engine analysis; the effect of the second law can now be quantified more precisely. Looking beyond the concept of an engine that alternates contact between heat baths of different temperature, one realizes that naturally occurring processes harvest energy from temperature or chemical gradients instead. Indeed, life on earth is sustained by the 6000K-300K gradient between the sun and the stary sky. The enabling mechanism for transduction of energy relies on non-equilibrium processes. In the talk we will explain how the theory of optimal mass transport provides the geometric setting for studying finite-time thermodynamic transitions and understanding energy harvesting mechanisms in an anisotropic environement. In particular, for a suitable model of a nonequilibrium process, known as the Brownian gyrator, we quantify for the first time maximal power and efficiency that can be attained by siphoning work out of a temperature gradient. In this context, dissipation and work output are expressed as path and area integrals, respectively, and fundamental limitations on power and eficiency are bounded by way of geometric isoperimetric inequalities. The analysis presented provides guiding principles for building autonomous engines that extract work from thermal or chemical anisotropy in the environment. A physical embodiment of such a thermal engine will be discussed, feeding on Nyquist-Johnson thermal noise gradients, and linked to the design of Stirling engines that can be understood from this same new angle.

Bio:
Tryphon T. Georgiou was educated at the National Technical University of Athens, Greece (Diploma 1979) and the University of Florida, Gainesville (PhD. 1983).  He is a Distinguished Professor at the Department of Mechanical and Aerospace Engineering, University of California, Irvine, and Professor Emeritus at the University of Minnesota. He is a Fellow of IEEE, SIAM, IFAC, AAAS and a Foreign Member of the Royal Swedish Academy of Engineering Sciences (IVA).