Currency can be considered as a ruler for values of commodities. Then the price is the measured value by the ruler. We can suppose that inflation and variation of exchange rate are caused by variation of the scale of the ruler. In geometry, variation of the scale means that the metric is...

The Fokker-Planck equation of a system of several Brownian particles immersed in a non-equilibrium bath of light particles is derived from first principles of statistical mechanics using time-dependent projection operators. The Fokker-Planck equation contains the usual equilibrium streaming and...

We study H-theorems associated with the Brownian motion with constant drift on the hyperbolic plane. Since this random process satisfies a linear Fokker–Planck equation, it is easy to show that, up to a proper scaling, its Shannon entropy is increasing over time. As a consequence, its...

We consider an exactly soluble model of a set of coupled harmonic oscillators, which was presented in a previous work. We show numerical results for the time evolution of the main dynamical quantities and compare them with analytical results.

Brownian motion of a parametric oscillator with asymmetric square waves which take a spring constant during a given length of time and suddenly change to a different value with a different length of time-duration has been investigated analytically with a view to the Paul trap in contrast to...

We analyze an equilibrium classical diffusion of a Brownian particle confined to a ring coated on a two-dimensional disordered film. The random potential modeling the interaction with the inhomogeneous medium is assumed to be Gaussian with a finite correlation length. With a microscopic method,...

Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by time-dependent drift and diffusion coefficients. Modeling such...

We consider different models of stochastic dissipative equations and theoretically compute the probability distribution functions (actually the associated large deviation functions) of the time averaged injected power required to sustain a nontrivial stationary state. We discuss the results and...

We study the effect of a field on the span of a particle diffusing on a line, i.e., the length covered by a Brownian particle which moves on a line for time t in the presence of a constant field. This is the one-dimensional analog of the Wiener sausage volume. Exact expressions are found for the...

High-frequency returns of the DAX German blue chip stock index are used to test geometric Brownian motion, the standard model for financial time series. Even on a 15-s time scale, the linear correlations of DAX returns have a zero-time delta function which carries 90% of the weight, while the...