Distinguished Lecture——Gallavotti–Cohen fluctuation theorem: Universal law of non-equilibrium statistical mechanics
报告人：Armen Shirikyan (CY Cergy Paris University)
时间：2025-05-30 14:00-15:00
地点：智华楼四元厅
Abstract: The irreversible behaviour of macroscopic processes governed by reversible laws of classical or quantum physics has been a captivating subject in statistical mechanics going back at least to the pioneering work of Boltzmann. The general consensus reached by the middle of the last century was that the second law of thermodynamics, which states that entropy increases with time, is empirical in nature, and that the probability of a negative fluctuation of entropy is so small that it cannot be observed in practice. A natural question is the quantitative description of that claim. A breakthrough on this subject came in the middle of nineties due to the work of Evans-Searles and Gallavotti-Cohen.
In this talk, I shall illustrate their discovery on the simplest example of finite state Markov chains. It will be shown that, under some natural hypotheses, one can define an entropy production observable whose time averages satisfy the large deviation principle. The resulting rate function possesses a symmetry property which implies that the probability of a negative value for the mean entropy production is exponentially suppressed by that of the opposite positive value. I shall also briefly discuss the current state of the realisation of this programme in the context of fluid flows.
Bio: A. Shirikyan received his Ph.D. from Moscow State University in 1995. He worked as a junior scientist at the Institute of Mechanics (Moscow) and as a research associate at Heriot-Watt University (Edinburgh) before joining the faculty of the University of Paris-Sud in 2002. Shirikyan has been a professor at CY Cergy Paris University since 2006 and an adjunct professor at McGill University since 2017. He served as department head from 2008 to 2012, director of the master's programme from 2015 to 2019, and is currently director of the CY Institute for Advanced Studies. Shirikyan's main contributions to mathematics concern the qualitative theory of hyperbolic PDEs, the long-time behaviour of random dynamical systems, control theory for PDEs, and some aspects of non-equilibrium statistical mechanics.
