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Fluctuation theorems based on time-reversal have provided remarkable insight into the non-equilibrium statistics of thermodynamic quantities like heat, work, and entropy production. These types of laws impose constraints on the…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…
The question of deriving general force/flux relationships that apply out of the linear response regime is a central topic of theories for nonequilibrium statistical mechanics. This work applies an information theory perspective to compute…
We study the one-point probability distribution functions (PDFs) of the peculiar velocity and the density fluctuation in a cosmological fluid. Within the perturbative approach to the structure formation scenario, the effect of ``pressure''…
Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…
Stationary solutions to a Fokker-Planck equation corresponding to a noisy logistic equation with correlated Gaussian white noises are constructed. Stationary distributions exist even if the corresponding deterministic system displays an…
We consider the response of a dynamical system driven by external adiabatic fluctuations. Based on the `adiabatic following approximation' we have made a systematic separation of time-scales to carry out an expansion in $\alpha |\mu|^{-1}$,…
Many-body quantum systems in nonequilibrium remain one of the frontiers of many-body physics. While there has been significant advances in describing the short-time evolution of these systems using a variety of different numerical…
A finite quantum system evolving unitarily equilibrates in a probabilistic fashion. In the general many-body setting the time-fluctuations of an observable \mathcal{A} are typically exponentially small in the system size. We consider here…
We address the effect of stochastic resetting on diffusion and subdiffusion process. For diffusion we find that MSD relaxes to a constant only when the distribution of reset times possess finite mean and variance. In this case, the leading…
We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady-state by using joint probability distributions symmetries of different entropy production decompositions. The analytical approach is…
The non-Gaussian normal diffusion, i.e., the probability distribution function (PDF) is non-Gaussian but the mean squared displacement (MSD) depends on time linearly, has been observed in particle motions. Here we show by numerical…
The method of photon distribution function (PDF) is used to study fluctuations of light beams propagating through a turbulent atmosphere. Our analysis concerns the regime of saturated fluctuations. The focus is on the phenomena of beam…
We develop a new computational framework to solve the partial differential equations (PDEs) governing the flow of the joint probability density functions (PDFs) in continuous-time stochastic nonlinear systems. The need for computing the…
Probability Distributions Functions (PDFs) of fluctuations of plasma edge parameters are skewed curves fairly different from normal distributions, whose shape appears almost independent of the plasma conditions and devices. We start from a…
The precision of reaction-diffusion models for mesoscopic physical systems is limited by fluctuations. To account for this uncertainty, Van Kampen derived a stochastic Langevin-like reaction-diffusion equation that incorporates…
For systems in equilibrium at a temperature $T$, thermal noise and energy damping are related to $T$ through the fluctuation-dissipation theorem (FDT). We study here an extension of the FDT to an out of equilibrium steady state: a…
We study fluctuations in diffusion-limited reaction systems driven out of their stationary state. Using a numerically exact method, we investigate fluctuation ratios in various systems which differ by their level of violation of microscopic…
A central problem in population ecology is understanding the consequences of stochastic fluctuations. Analytically tractable models with Gaussian driving noise have led to important, general insights, but they fail to capture rare,…
We investigate the time behavior of the fragmentation model with Kolmogorov time scales and space contraction resembling the random $\beta$-model of turbulence. The space averages computed at any instant using the entire spatial realization…