We made a first attempt to associate a probabilistic description of stochastic processes like birth–death processes with spacetime geometry in the Schwarzschild metrics on distance scales from the macro- to the micro-domains. We idealize an ergodic system in which system states communicate...

We study chaotic functions that are exact solutions to nonlinear maps. A generalization of these functions (which cannot be expressed as a recursive procedure anymore) can produce truly random sequences. Even if the initial conditions are known exactly, the next values are in principle...

The motion of a particle confined within a strip (“flat pipe”) with diffusely-reflecting walls is analyzed in detail and provides a simple example of the interplay between randomness and geometrical constraint. The mean square dispersion Δx2 of the position is exactly found in various...