Alberto Rosso

We show that nonequilibrium dynamics can play a constructive role in unsupervised machine learning by inducing the spontaneous emergence of latent-state cycles. We introduce a model in which visible and hidden variables interact through two independently parametrized transition matrices, defining a Markov chain whose steady state is intrinsically out of equilibrium. Likelihood maximization drives this system toward nonequilibrium steady states with finite entropy production, reduced self-transition probabilities, and persistent probability currents in the latent space. These cycles are not imposed by the architecture but arise from training, and models that develop them reproduce the empirical distribution of data classes more faithfully, with a clear correlation between agreement with the data and entropy production. Compared with equilibrium approaches such as restricted Boltzmann machines, our model breaks the detailed balance between the forward and backward conditional transitions and relies on a log-likelihood gradient that depends explicitly on the last two steps of the Markov chain. Hence, this exploration of the interface between nonequilibrium statistical physics and modern machine learning suggests that introducing irreversibility into latent-variable models can improve the fidelity of the generated data distribution.

We investigate the dynamics of a run-and-tumble particle in a double-well potential and demonstrate that, in stark contrast to Brownian particles, active dynamics can lead to strong ergodicity breaking. When the barrier height exceeds a critical threshold, the long-time position distribution depends crucially on the initial condition: If the particle starts within the basin of attraction of one well, it remains trapped there, while if it begins between the two basins, it can reach either well with a finite probability, which we compute exactly via hitting probabilities. Below the critical barrier height, ergodicity is restored and the system converges to a unique stationary distribution, which we derive analytically. Using this result, we also estimate the characteristic barrier-crossing time and show that it violates Kramers-Arrhenius law and displays a divergence near the critical height following a Vogel-Fulcher-Tammann-like form with an anomalous exponent 1 / 2 .

We study a continuous time branching process where an individual splits into two daughters with rate b and dies with rate a , starting from a single individual at t = 0. This model can be mapped exactly to a random walk problem where the population size N ( t ) performs a random walk on a positive semi-infinite lattice. The hopping rate of this random walker out of a site labeled n is proportional to n , i.e. the walker gets more and more ‘active’ or ‘agitated’ as it moves further and further away from the origin–we call this an ‘agitated random walk’. We demonstrate that this random walk problem is particularly suitable to obtain exact explicit results on the extreme value statistics, namely, on the distribution of the maximal population size M ( t ) = max 0 ⩽ τ ⩽ t [ N ( τ ) ] up to time t . This extreme value distribution displays markedly different behaviors in the three phases: (i) subcritical ( b < a ) (ii) critical ( b = a ) and (iii) supercritical ( b > a ) . In the subcritical phase, Q ( L , t ) becomes independent of time t for large t and the stationary distribution Q ( L , ∞ ) decays exponentially with increasing L . At the critical point b = a , the distribution again becomes independent of t for large t , but the stationary distribution Q ( L , ∞ ) ∼ 1 / L 2 has a power law tail for large L . For finite but large t , the distribution at the critical point exhibits a scaling form Q ( L , t ) ∼ f c ( L / a t ) / L 2 where the scaling function f c ( z ) has a nontrivial shape that we compute analytically. In the supercritical phase, the distribution Q ( L , t ) has a ‘fluid’ part that becomes independent of t for large t and a ‘condensate’ part (a delta peak centered at e ( b − a ) t ) which gets disconnected from the ‘fluid’ part and moves rapidly to ∞ as time increases. We also verify our analytical predictions via numerical simulations finding excellent agreement. Our results can be applied to characterize the time dependence of the size of the maximally infected population up to a fixed time during an epidemic spread.

Disordered systems under applied loading display slow creep flows at finite temperature. Renormalization group arguments predicted that creep proceeds via thermal avalanches of activated events. Recently, thermal avalanches were argued to control the dynamics of liquids near their glass transition. Both theoretical approaches are markedly different. Here we provide a scaling description that seeks to unify dynamical heterogeneities in both phenomena, confirm it in simple models of pinned elastic interfaces, and discuss its experimental implications.

In this paper, we consider the problem of numerical investigation of the counting statistics for a class of one-dimensional systems. Importance sampling, the cornerstone technique usually implemented for such problems, critically hinges on selecting an appropriate biased distribution. While an exponential tilt in the observable stands as the conventional choice for various problems, its efficiency in the context of counting statistics may be significantly hindered by the genuine discreteness of the observable. To address this challenge, we propose an alternative strategy, which we call importance sampling with the local tilt. We demonstrate the efficiency of the proposed approach through the analysis of three prototypical examples: a set of independent Gaussian random variables, Dyson gas, and symmetric simple exclusion process with a steplike initial condition.