Finding the Effective Dynamics to Make Rare Events Typical in Chaotic Maps.

Dynamical fluctuations or rare events associated with atypical trajectories in chaotic maps due to specific initial conditions can crucially determine their fate, as the may lead to stability islands or regions in phase space otherwise displaying unusual behavior. Yet, finding such initial conditions is a daunting task precisely because of the chaotic nature of the system. In this Letter, we circumvent this problem by proposing a framework for finding an effective topologically conjugate map whose typical trajectories correspond to atypical ones of the original map.

Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents.

The study of dynamical large deviations allows for a characterization of stationary states of lattice gas models out of equilibrium conditioned on averages of dynamical observables. The application of this framework to the two-dimensional random walk conditioned on partial currents reveals the existence of a dynamical phase transition between delocalized band dynamics and localized vortex dynamics. We present a numerical microscopic characterization of the phases involved and provide analytical insight based on the macroscopic fluctuation theory.

Symmetry-induced fluctuation relations in open quantum systems.

We derive a general scheme to obtain quantum fluctuation relations for dynamical observables in open quantum systems. For concreteness, we consider Markovian nonunitary dynamics that is unraveled in terms of quantum jump trajectories and exploit techniques from the theory of large deviations like the tilted ensemble and the Doob transform. Our results here generalize to open quantum system fluctuation relations previously obtained for classical Markovian systems and add to the vast literature on fluctuation relations in the quantum domain, but without resorting to the standard two-point measurement scheme.

Generalized optimal paths and weight distributions revealed through the large deviations of random walks on networks.

Numerous problems of both theoretical and practical interest are related to finding shortest (or otherwise optimal) paths in networks, frequently in the presence of some obstacles or constraints. A somewhat related class of problems focuses on finding optimal distributions of weights which, for a given connection topology, maximize some kind of flow or minimize a given cost function. We show that both sets of problems can be approached through an analysis of the large-deviation functions of random walks.

Entanglement statistics in Markovian open quantum systems: A matter of mutation and selection.

Controlling dynamical fluctuations in open quantum systems is essential both for our comprehension of quantum nonequilibrium behavior and for its possible application in near-term quantum technologies. However, understanding these fluctuations is extremely challenging due, to a large extent, to a lack of efficient important sampling methods for quantum systems. Here, we devise a unified framework-based on population-dynamics methods-for the evaluation of the full probability distribution of generic time-integrated observables in Markovian quantum jump processes.

Symmetry-induced fluctuation relations for dynamical observables irrespective of their behavior under time reversal.

We extend previous work to describe a class of fluctuation relations (FRs) that emerge as a consequence of symmetries at the level of stochastic trajectories in Markov chains. We prove that given such a symmetry, and for a suitable dynamical observable, it is always possible to obtain a FR under a biased dynamics corresponding to the so-called generalized Doob transform. The general transformations of the dynamics that we consider go beyond time-reversal or spatial isometries, and an implication is the existence of FRs for observables irrespective of their behavior under time reversal, for example for time-symmetric observables rather than currents.

Sampling rare events across dynamical phase transitions.

Interacting particle systems with many degrees of freedom may undergo phase transitions to sustain atypical fluctuations of dynamical observables such as the current or the activity. In some cases, this leads to symmetry-broken space-time trajectories which enhance the probability of such events due to the emergence of ordered structures. Despite their conceptual and practical importance, these dynamical phase transitions (DPTs) at the trajectory level are difficult to characterize due to the low probability of their occurrence.

Fluctuating hydrodynamics, current fluctuations, and hyperuniformity in boundary-driven open quantum chains.

We consider a class of either fermionic or bosonic noninteracting open quantum chains driven by dissipative interactions at the boundaries and study the interplay of coherent transport and dissipative processes, such as bulk dephasing and diffusion. Starting from the microscopic formulation, we show that the dynamics on large scales can be described in terms of fluctuating hydrodynamics. This is an important simplification as it allows us to apply the methods of macroscopic fluctuation theory to compute the large deviation (LD) statistics of time-integrated currents.

Epidemic Dynamics in Open Quantum Spin Systems.

We explore the nonequilibrium evolution and stationary states of an open many-body system that displays epidemic spreading dynamics in a classical and a quantum regime. Our study is motivated by recent experiments conducted in strongly interacting gases of highly excited Rydberg atoms where the facilitated excitation of Rydberg states competes with radiative decay. These systems approximately implement open quantum versions of models for population dynamics or disease spreading where species can be in a healthy, infected or immune state.

Infinite family of second-law-like inequalities.

The probability distribution function for an out of equilibrium system may sometimes be approximated by a physically motivated "trial" distribution. A particularly interesting case is when a driven system (e.g.

Symmetries in fluctuations far from equilibrium.

Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space.