Statistical Mechanics

Optimal transport is a mathematical method to define a distance between probability distributions. This is particularly useful in various domains, including physics, biology, machine learning, and economics, among others. After introducing the Optimal Transport (OT) problem at finite temperature, we show how it can be formulated as a statistical physics problem. This approach allows us to derive very efficient algorithms to effectively compute the distance between two probability distributions. The a priori unrelated Schrödinger bridge (SB) problem is presented, and it is shown to be a dynamical version of the optimal transport problem. Indeed, the Schrodinger bridge looks for the most probable path in probability distribution space, which connects two given probabilities. The Schrodinger bridge problem, originally devised for freely diffusing particles, can be generalized to the case of interacting particles. It can be formulated in terms of functional integrals over bosonic fields, which allows us to derive partial differential equations that characterize the most probable paths in probability space. CARL VAN VREESWIJK MEMORIAL LECTURE 2026. Presented in the van Vreeswijk Theoretical Neuroscience Seminar series (formerly WWTNS) on 2026-04-15. Recording duration: 00:55:05.

Three two-year postdoctoral positions investigate the origins of irreversible behaviour through mathematical physics, theoretical physics and the history of physics. Topics include entropy, randomness, statistical mechanics, gravitational and holographic systems, and the historical development of chaos. Researchers join the Radboud Center for Natural Philosophy and collaborate across disciplines. The full-time gross monthly salary is EUR 3,706–5,760, according to experience. Apply by 14 October 2026 with a motivation letter, CV/publications, three referees and the position or positions sought. The preferred start is 1 January 2027, with an agreed later start possible up to 1 September 2027.

Three two-year postdoctoral positions investigate the origins of irreversible behaviour through mathematical physics, theoretical physics and the history of physics. Topics include entropy, randomness, statistical mechanics, gravitational and holographic systems, and the historical development of chaos. Researchers join the Radboud Center for Natural Philosophy and collaborate across disciplines. The full-time gross monthly salary is EUR 3,706–5,760, according to experience. Apply by 14 October 2026 with a motivation letter, CV/publications, three referees and the position or positions sought. The preferred start is 1 January 2027, with an agreed later start possible up to 1 September 2027.