Speaker
Description
The theory of martingales played a key role in the development of probability theory and stochastic processes. For instance, it allowed to prove convergence theorems generalizing the central limit theorems, that are central also in physics. Furthermore, martingales played a key role in quantitative finance, setting the fundamental theorems of finance that rationalize Black-Scholes model for financial markets. In nonequilibrium statistical physics, the usage of martingales is quite recent yet insightful to establish new universal thermodynamic principles. In this talk, I will review pioneering efforts in developing a "martingale thermodynamics theory" to tackle nonequilibrium fluctuations of small systems. In particular, I will explain how this theory is fruitful in providing extreme-value and stopping-time statistics for entropy production, and sketch some experimental verifications. I will also overview how can one use clever stopping (e.g. first passage) strategies to overcome classical limits such as Carnot efficiency at the expense of efficient, yet still unorthodox, information processing schemes.
[1] Martingales for physicists: A treatise on stochastic thermodynamics and beyond, E Roldan, I Neri, R Chetrite, S Gupta, S Pigolotti, F Jülicher, K Sekimoto, arXiv:2210.09983 (2022) ; Advances in Physics - in press (2024)
