February 9, 2024 Season 2023-2024 Main speaker: N. Kistler

February 9, 2024

Location: Janskerkhof 2-3 , room 115
Tristan Benoist (Tolouse ) homepage

On repeated quantum measurements: limit theorems, entropy production and hypothesis testing of the arrow of time

In quantum mechanics, the result of a measurement is intrinsically random and induces a back-action on the measured system. The resulting law of a sequence of (indirect) measurements is a generalisation of hidden markov models. They form a weakly dense set of probability measures distinct from the set of weak Gibbs measures while still accessible through thermodynamic formalism. Motivated by physics, I am interested in understanding the large time properties of the related dynamical system. Depending on time, in this presentation I will define the probability measures involved and review some results on limit theorems (law of large numbers, central limit theorem, large deviation principle…). I will present the two main standard strategy of proof. I will then present an original approach we developed with some collaborators using sub-additivity to study the entropy production associated with the repeated measurement dynamical system. I will explain how these result can be used to formalise the hypothesis testing of the arrow of time and how it relates to out of equilibrium thermodynamics.

Simone Baldassarri (Florence) homepage

Homogeneous nucleation for two-dimensional Kawasaki dynamics

We study a lattice gas subject to Kawasaki dynamics at inverse temperature $\beta>0$ in a large finite box $\Lambda_\beta \subset \mathbb{Z}^2$ of size $|\Lambda_\beta| = e^{\Theta\beta}$, with $\Theta>0$. Each pair of neighbouring particles has a negative binding energy $-U<0$, while each particle has a positive activation energy $\Delta>0$. The initial configuration is drawn from the grand-canonical ensemble restricted to the set of configurations where all the droplets are subcritical. Our goal is to describe, in the metastable regime $\Delta \in (U,2U)$ and in the limit as $\beta\to\infty$, how and when the system nucleates, i.e., creates a critical droplet somewhere in $\Lambda_\beta$ that subsequently grows by absorbing particles from the surrounding gas. We will see that in a very large volume ($\Theta> 2\Delta-U$) critical droplets appear more or less independently in boxes of moderate volume ($\Theta< 2\Delta-U$), a phenomenon referred to as homogeneous nucleation. This is a joint work with Alexandre Gaudillière, Frank den Hollander, Francesca Romana Nardi, Enzo Olivieri and Elisabetta Scoppola.