Related papers: The law of series
A version of the second law of thermodynamics states that one cannot lower the energy of an isolated system by a cyclic operation. We prove this law without introducing statistical ensembles and by resorting only to quantum mechanics. We…
The second law of thermodynamics is asymmetric with respect to time as it says that the entropy of the universe must have been lower in the past and will be higher in the future. How this time-asymmetric law arises from the time-symmetric…
We study returns in dynamical systems: when a set of points, initially populating a prescribed region, swarms around phase space according to a deterministic rule of motion, we say that the return of the set occurs at the earliest moment…
We study convergence of return- and hitting-time distributions of small sets $E_{k}$ with $\mu(E_{k})\rightarrow0$ in recurrent ergodic dynamical systems preserving an infinite measure $\mu$. Some properties which are easy in finite measure…
The arrow of time is an irreversible phenomenon for a system of particles undergoing reversible dynamics. Since the time of Boltzmann to this day, the arrow of time has led to debate and research. However, the enormous growth of…
In classical physics the joint probability of a number of individually rare independent events is given by the Poisson distribution. It describes, for example, unidirectional transfer of population between the densely and sparsely populated…
Dynamical processes can be classified in various ways as deterministic or stochastic, and continuous or discrete time. All these types can be studied by the path-spaces they generate, and stationary measures on that path-space. Such…
It is a common belief that in any environment where life is possible, life will be generated. Here it is suggested that the cause for a spontaneous generation of complex systems is probability driven processes. Based on equilibrium…
We treat a quantum mechanical system with certain general properties which are expected to be common in macroscopic quantum systems. Starting from a PURE initial state (which may not describe an equilibrium) in which energy is mildly…
In this paper we study the distribution of hitting and return times for observations of dynamical systems. We apply this results to get an exponential law for the distribution of hitting and return times for rapidly mixing random dynamical…
The first-passage time is proposed as an independent thermodynamic parameter of the statistical distribution that generalizes the Gibbs distribution. The theory does not include the determination of the first passage statistics itself. A…
We study the entropy production of a system with a finite number of states connected by random transition rates. The stationary entropy production, driven out of equilibrium both by asymmetric transition rates and by an external probability…
The distribution of recurrence times or return intervals between extreme events is important to characterize and understand the behavior of physical systems and phenomena in many disciplines. It is well known that many physical processes in…
We analyze the asymptotic behavior of sequences of random variables defined by an initial condition, a stationary and ergodic sequence of random matrices, and an induction formula involving multiplication is the so-called max-plus algebra.…
We investigate continuous time random walks with truncated $\alpha$-stable trapping times. We prove distributional ergodicity for a class of observables; namely, the time-averaged observables follow the probability density function called…
We study the rare event behavior of the workload process in a transitory queue, where the arrival epochs (or points) of a finite number of jobs are assumed to be the ordered statistics of independent and identically distributed (i.i.d.)…
We give a generalization of the ergodic theorem for semi-Markov linear-type processes. This generalization is proved for the case when a common support of distributions defining this process is not arithmetic. Also we give an uniform…
We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where…
We show that the probability distribution function that best fits the distribution of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space deviates from the exponential statistics by a…
Consider the random process that starts with $n$ vertices and no edges, where the edges of $K_n$ are added one at a time in a uniformly chosen random order $e_1, e_2,\ldots, e_{\binom{n}{2}}$. Let $T$ be the earliest time at which $e_1$…