The form of the reaction rates in the birth-and-death formalism of a chemical reaction is obtained by applying the principle of stationarity of the thermodynamic equilibrium distribution.

By using the spectral theory of the master equation, it is shown generally that a self-catalytic chemical system may evolve according to two widely different time scales in this case. The shorter one describes the evolution towards a quasi-stationary state which is the stochastic equivalent of...

In a previous communication the Boltzmann equations for a bimolecular chemical reaction were transformed into an infinite system of quadratic differential equations. It is shown here that the reaction rate may be calculated approximately by using the first differential equation only, which is a...

We propose a new model of 2D free particle diffusion on a possibly curved surface. This model is a generalization of the standard Ornstein–Uhlenbeck process and is completely determined by writing down the transport equation describing the diffusion in the phase-space of the diffusing...

A stochastic model is proposed to take into account the effect of a weak external field associated to diffusion, a discrete Master Equation is written down for the spatial distribution of particles. Approximate solutions are found for the first two cumulants, and applied to an example of...

A cellular automation model is used to describe the dynamics of the catalytic oxidation of CO on a Pt(1 0 0) surface. The cellular automation rules account for the structural phase transformations of the Pt substrate, the reaction kinetics of the adsorbed phase and diffusion of adsorbed species....

The application of the Onsager-Machlup principle to non-linear fluctuations of a thermodynamic variable is discussed. The Onsager law of proportionality of fluxes and forces is obtained by an integral method. Approximate calculation of the transition probabilities and of the most probable...

The best way of finding a hidden target is a general question which concerns many fields of natural and social sciences. It is of vital importance for foraging animals. It has been observed that many species adopt an intermittent behaviour, alternating phases of intensive search and slow...

We present a stochastic study of a polymerization reaction model. Using the WKB approximation and the method of factorial cumulants it is shown that the relaxation time of the second factorial cumulant is half the macroscopic relaxation time. Furthermore the system exhibits a globally...