Related papers: Time irreversibility and amplitude irreversibility…
The training algorithms for AI systems all introduce far-from-equilibrium dynamical processes, and understanding the irreversibility of these algorithms is a fundamental step towards understanding the learning dynamics of modern AI systems.…
We study a classical reparametrization-invariant system, in which ``time'' is not a priori defined. It consists of a nonrelativistic particle moving in five dimensions, two of which are compactified to form a torus. There, assuming a…
We study dynamical reversibility in stationary stochastic processes from an information theoretic perspective. Extending earlier work on the reversibility of Markov chains, we focus on finitary processes with arbitrarily long conditional…
A sequence of moments encode the corresponding probability distribution. Probing if quantum joint probability distribution can be retrieved from the associated set of moments -- realized in the sequential measurement of a dichotomic…
The issue of irreversibility in a universe with time-reversal-symmetric laws is a central problem in physics. % , and, in particular, to statistical mechanics, information theory and quantum thermodynamics. In this letter, we discuss for…
In this article we look at stochastic processes with uncertain parameters, and consider different ways in which information is obtained when carrying out observations. For example we focus on the case of a the random evolution of a traded…
The time reversal method in thermoacoustic tomography is used for approximating the initial pressure inside a biological object using measurements of the pressure wave made on a surface surrounding the object. This article presents error…
In this work we present a re-evaluation of the concept of time in non-relativistic quantum theory. We suggest a formalism in which time is changed into the status of an operator, and where expectation values of observables and the state of…
This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong…
We are concerned with three types of uncertainties: probabilistic, possibilitistic and interval. By using possibility and necessity measures as an Interval Valued Probability Measure (IVPM), we present IVPM's interval expected values whose…
We obtain universal estimates on the convergence to equilibrium and the times of coupling for continuous time irreducible reversible finite-state Markov chains, both in the total variation and in the L^2 norms. The estimates in total…
We examine a family of intrinsic performance measures in terms of probability distributions that generalize Hellinger distance and Fisher information. They are applied to quantum metrology to assess the uncertainty in the detection of…
The creativity and emergence of biological and psychological behavior are nonlinear. However, that does not necessarily mean only that the measurements of the behaviors are curvilinear. Furthermore, the linear model might fail to reduce…
The quantization of time-reparametrization invariant systems such as general relativity is plagued by an ambiguity relating to the role of time in the theory. If one parametrizes observables by the (unobservable) time, and then relies on…
Quantum measurement is a fundamental concept in the field of quantum mechanics. The action of quantum measurement, leading the superposition state of the measured quantum system into a definite output state, not only reconciles…
The entropy production is commonly interpreted as measuring the distance from equilibrium. However, this explanation lacks a rigorous description due to the absence of a natural equilibrium measure. The present analysis formalizes this…
The aim of sequential change-point detection is to issue an alarm when it is thought that certain probabilistic properties of the monitored observations have changed. This work is concerned with nonparametric, closed-end testing procedures…
For theoretical approach of quantum measurements it is proposed a set of reconsidered conjectures. The proposed approach implies linear functional transformations for probability density and current but preserves the expressions for…
Time can be defined as the duration between events. It is irreversible. When used as a variable in quantifying the changing properties of matter, this irreversibility of time is incompatible with Newton's deterministic mechanics and with…
Three aspects of time series are uncertainty (dispersion at a given time scale), scaling (time-scale dependence), and intermittency (inclination to change dynamics). Simple measures of dispersion are the mean absolute deviation and the…