Monday, 28 September 2026
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I will discuss two settings where the variational problem within MFT can be solved to yield explicit results on nonequilibrium fluctuations. The first concerns tracer and current statistics in a single-file gas of Brownian hard rods. Exploiting a duality with a point-particle system, we exactly compute the cumulant-generating functions and optimal fluctuation paths for two domain-wall initial ensembles. Our results reveal an intriguing connection with the height field of the dual point-particle system, linking single-file transport to interface dynamics. The second concerns steady-state density large deviations in boundary-driven diffusive systems with a bulk drive. Using an auxiliary-field transformation, we obtain perturbative results for generic systems, including in arbitrary dimensions. Our formulation reveals the dynamical origin of long-range correlations in the steady state and how the onset of non-locality depends on the bulk drive.
Over the past two decades, the Macroscopic Fluctuation Theory (MFT) has provided a universal framework to deal with classical diffusive non-equilibrium systems. A natural question is whether this framework can be extended to quantum mechanics to capture the statistics of inherently quantum phenomena, such as interference and entanglement, in diffusive, out-of-equilibrium systems. In this talk, we first review key insights from model systems, including Quantum Exclusion Processes. We then present recent progress toward formulating a Quantum Mesoscopic Fluctuation Theory (QMFT) and conclude by outlining the open challenges and steps required to achieve a comprehensive theory.
Tuesday, 29 September 2026
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.
“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.
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).
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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Wednesday, 30 September 2026
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We show the relationship between the strongly non-linear limit (also termed the dispersionless or the Whitham limit) of the macroscopic fluctuation theory of certain statistical models and the inverse scattering method. We show that in the strongly non-linear limit the inverse scattering problem can be solved using the steepest descent method of the associated Riemann–Hilbert problem. The form of the strongly-nonlinear theory serves as a formal classification scheme for the different models studied using large fluctuation theory that exhibit integrability.
We study the current fluctuations of the one-dimensional symmetric exclusion process evolving under a quenched initial condition. The macroscopic fluctuation theory is employed to probe the fluctuations and it is subsequently reformulated in terms of the potential in the inverse scattering method, leading to the boundary equation that determines the final profile of the potential. Then, we solve this nonlinear functional integral equation by applying the perturbation method up to the sufficient order to compute the fourth cumulant.
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Thursday, 01 October 2026
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We discuss the ergodicity of quantum Markov semigroups in terms of trace distance from the stationary state.
While Macroscopic Fluctuation Theory (MFT) has been highly successful in analyzing non-equilibrium steady states, its application to non-steady-state processes remains limited. In this talk, we will present our MFT analysis of the relaxation process of one-dimensional boundary-driven diffusive systems coupled to particle reservoirs at both ends. We derive the MFT action for the integrated current and obtain the corresponding MFT equations, together with their initial and boundary conditions. Using this formulation, we exactly derive the current variance for systems with a constant diffusion coefficient and arbitrary mobility, and the cumulant generating function for the current in Reflective Brownian Motion (RBM). Our results demonstrate that non-steady current fluctuations during the approach to a steady state can be quantitatively described within the MFT framework. This talk is based on joint work with Tomohiro Sasamoto (arXiv:2605.27275).
A measure of similarity or overlap between different configurations or individuals appears in many complex systems such as spin glasses, evolving populations, optimization problems and neural networks. In the context of spin glasses, the concept was introduced by Edwards and Anderson 50 years ago and gives a measure of similarity between pairs of spin configurations. In the context of evolving populations, the overlap measures the similarity between genomes of individuals. In general the overlaps fluctuate and have non-trivial statistics. Giorgio Parisi's replica theory of mean field spin glasses predicted a universal form for the overlap statistics. In this talk I will compare these predictions with the statistics for different models of disordered systems and for evolving populations.