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The role of memory time fluctuations for instabilities in random media is considered. It is shown that fluctuations can result in infinitely fast growth of statistical moments. The effect is demonstrated in the framework of light…

We present a unifying framework to the understanding of when and how quantum mechanical systems become independent of their initial conditions and adapt macroscopic properties (like temperature) of the environment.By viewing this problem…

We investigate the effect of memory terms on the entropy decay of the solutions to equations with Ornstein-Uhlenbeck operators. Our assumptions on the memory kernels include Caputo-Fabrizio operators and, more generally, the stretched…

Decoherence is often modeled using Markovian master equations that predict exponential suppression of coherence and are frequently used as effective bounds on quantum behavior in complex environments. Such descriptions, however, correspond…

We investigate dynamical equilibration of expectation values in closed quantum systems for realistic non-equilibrium initial states. Thereby we find that the corresponding long time expectation values depend on the initial expectation…

With a statistical measure of distance, we derive a classical uncertainty relation for processes traversing nonequilibrium states both transiently and irreversibly. The geometric uncertainty associated with dynamical histories that we…

Understanding temporal processes and their correlations in time is of paramount importance for the development of near-term technologies that operate under realistic conditions. Capturing the complete multi-time statistics defining a…

Any repeated use of a fixed experimental instrument is subject to memory effects. We design an estimation method uncovering the details of the underlying interaction between the system and the internal memory without having any experimental…

The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled…

Primordial gravitational waves, after they enter the horizon and decay away, leave a residual displacement in test particles: a memory, in analogy with gravitational waves generated by astrophysical sources. The late-time distance between…

We consider a model of Brownian motion on a bounded open interval with instantaneous jumps. The jumps occur at a spatially dependent rate given by a positive parameter times a continuous function positive on the interval and vanishing on…

We analyse the long-lasting effects of initial conditions on fluctuations in one-dimensional diffusive systems. We consider both the fluctuations of current for non-interacting diffusive particles starting from a step-like initial density…

We consider a discrete-time random walk where the random increment at time step $t$ depends on the full history of the process. We calculate exactly the mean and variance of the position and discuss its dependence on the initial condition…

We point out that even at the absolute zero of temperature environmental decoherence limits the destructive interference between time-reversed paths for an electron in a disordered metal, and thus causes the leading (`weak localization')…

A major part of the many thermally driven processes in our natural environment as well as in engineering solutions of Carnot-type machinery is based on the second law of thermodynamics (or principle of entropy increase). An interesting link…

Quantum memory effects are essential in understanding and controlling open quantum systems, yet distinguishing them from classical memory remains challenging. We introduce a convex geometric framework to analyze quantum memory propagating…

Diffusive transport in many complex systems features a crossover between anomalous diffusion at short times and normal diffusion at long times. This behavior can be mathematically modeled by cutting off (tempering) beyond a mesoscopic…

Enhancing the precision of a thermodynamic process inevitably necessitates a thermodynamic cost. This notion was recently formulated as the thermodynamic uncertainty relation, which states that the lower bound on the relative variance of…

The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the…

We consider a Brownian particle which, in addition to being in contact with a thermal bath, is driven by fluctuating forces which stem from active processes in the system, such as self-propulsion or collisions with other active particles.…