Related papers: Microscopic Reversibility and Macroscopic Irrevers…

It has been a long time issue in statistical physics how to combine reversible microscopic equations with irreversible macroscopic behavior. Recently, Evans and Searles have suggested causality as the key concept for a solution to the…

A dynamical system is said to be reversible if, given an output, the input can always be recovered in a well-posed manner. Nevertheless, we argue that reversible systems that have a time-reversal symmetry, such as the Nonlinear…

Algorithmic Recourse (AR) aims to provide users with actionable steps to overturn unfavourable decisions made by machine learning predictors. However, these actions often take time to implement (e.g., getting a degree can take years), and…

The connection between the micro and macro-arrow of time is discussed in the frame of the stochastic quantum hydrodynamic analogy (SQHA). The presence of fluctuations that in the case on non-linear interactions leads to the breaking of the…

In relativistic theories the principle of microscopic causality states that ``information cannot travel faster than the speed of light'' \cite{kaku}. In the present work we show that the time evolution of relativistic wave functions…

This paper gives an overview of recent results concerning the long time dynamics of repeated interaction quantum systems in a deterministic and random framework. We describe the non equilibrium steady states (NESS) such systems display and…

We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…

We generalize the exact solution to the Bernoulli shift map. Under certain conditions, the generalized functions can produce unpredictable dynamics. We use the properties of the generalized functions to show that certain dynamical systems…

We consider simple exclusion processes on Z for which the underlying random walk has a finite first moment and a non-zero mean and whose initial distributions are product measures with different densities to the left and to the right of the…

Recently probabilistic hysteresis in isolated Hamiltonian systems of ultracold atoms has been studied in the limit of large particle numbers, where a semiclassical treatment is adequate. The origin of irreversibility in these sweep…

We employ a quantum macrostatistical treatment of irreversible processes to prove that, in nonequilibrium steady states, (a) the hydrodynamical observables execute a generalised Onsager-Machlup process and (b) the spatial correlations of…

Laws of large numbers guarantee that given a large enough sample from some population, the measure of any fixed sub-population is well-estimated by its frequency in the sample. We study laws of large numbers in sampling processes that can…

Historically time-reversibility of the transitions or processes underpinning Markov chain Monte Carlo methods (MCMC) has played a key r\^ole in their development, while the self-adjointness of associated operators together with the use of…

Recursive Monte Carlo filters, also called particle filters, are a powerful tool to perform computations in general state space models. We discuss and compare the accept--reject version with the more common sampling importance resampling…

Boltzmann's principleS=k*ln W is generalized to non-equilibrium Hamiltonian systems with possibly fractal distributions in phase space by the box-counting volume. The probabilities P(M) of macroscopic observables M are given by the ratio…

To understand the emergence of macroscopic irreversibility from microscopic reversible dynamics, the idea of coarse-graining plays a fundamental role. In this work, we develop a unified inferential framework for macroscopic states, that is,…

We investigate the robustness of the microscopic reversibility in open quantum systems which is discussed by Monnai [arXiv:1106.1982 (2011)]. We derive an exact relation between the forward transition probability and the reversed transition…

We shall show that the abstract and formal rules which govern the quantum kinematic and dynamics can be derived from a law of change of the information content or the degree of uncertainty that the system has a certain configuration in a…

We propose some new results on the comparison of the minimum or maximum order statistic from a random number of non-identical random variables. Under the non-identical set-up, with certain conditions, we prove that random minimum (maximum)…

We investigate temporal evolution of von Neumann's entropy in exemplary quantum mechanical systems and show that it grows in systems evolving with incrementally increasing decoherence during scattering processes. We demonstrate that the…