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09:30 to 11:30 |
Cristian Giardinà (Università di Modena e Reggio Emilia, Modena, Italy) |
Discrete macroscopic fluctuation theory and duality properties This pedagogical lecture will discuss a discrete formulation of macroscopic fluctuation theory (arising from the large-spin limit of interacting particle systems) and duality properties.
In the first part, I will introduce Markov duality and explain how it provides an effective tool for studying non-equilibrium stochastic systems. The harmonic process—an integrable model of heat conduction—will serve as the main example. I will review its algebraic structure and show how duality gives access to correlation functions and to an explicit characterization of the non-equilibrium stationary state. This exact microscopic information makes it possible to verify some predictions of macroscopic fluctuation theory, while suggesting the need for extensions to include singular profiles.
In the second part, I will discuss dynamical large deviations in the large-spin regime. For a large class of models, I will explain how a path-space large-deviation principle leads to a finite-dimensional Hamiltonian theory on the lattice—a discrete counterpart of the usual macroscopic fluctuation theory. The associated Hamilton equations and variational principles describe the optimal trajectories responsible for rare density and current fluctuations. I will conclude by discussing the connections among discrete and continuum MFT and fluctuation symmetries.
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14:30 to 15:10 |
Jorge Kurchan (Laboratoire de Physique de l'École Normale Supérieure (LPENS), CNRS, ENS, PSL, Paris, France) |
Liquid theory of spherical and unitary designs “Designs” are sets of points, for example on a sphere, that have the property that averages of polynomials over the set coincide with averages over the whole sphere. Similarly for the unitary group. One can treat these points as interacting particles, and use liquid theory to study the problem. Presented from a physicist's point of view.
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15:10 to 15:50 |
R. L. Jack (Department of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge, UK) |
Macroscopic fluctuation theory for active matter We consider exclusion processes as models for active matter systems, which undergo motility-induced phase separation [1] and as well dynamical pattern-forming behaviour [2]. I will present examples of phase transitions in these systems, as well as discussing the mechanisms for (rare) transitions between metastable states.
[1] Kourbane-Houssene, Erignoux, Bodineau and Tailleur, PRL 120, 268003 (2018).
[2] Mason, Jack, and Bruna, Nat Comms 16, 6017 (2025).
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15:50 to 16:30 |
Cesare Nardini (CEA Saclay, SPEC, France) |
Non-local stationary measures and nucleation theory in active systems In active systems detailed balance is broken at the level of each individual constituent. In this talk I will show that, in several cases, the probability of nucleating the stable state from a metastable one can be computed analytically although the instanton is not the time-reversal of the relaxation dynamics. We will furthermore discuss that their stationary measure can be generically expected to be non-local whenever at least one conservation law is present, and that this property has a surprising relation with nucleation probabilities. Our results will be mostly based on the weak-noise regime of a number of field theories that were proposed to describe active systems in the past.
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17:00 to 18:00 |
Cédric Bernardin (HSE University, Moscow, Russia) |
Generalizations of MFT: the long-range case |
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