In this note I introduce some techniques to treat systems in contact with (stochastic) thermal baths. The methods and the level of rigour are those of theoretical physics.

The dynamics of the approach to equilibrium of the hydrogen atom is investigated numerically through a Monte Carlo procedure. We show that, before approaching ionization, the hydrogen atom may live in a quasi-equilibrium state, characterized by aging, whose duration increases exponentially as...

We discuss a property of our recently introduced generalized canonical ensemble [M. Costeniuc, R.S. Ellis, H. Touchette, B. Turkington, The generalized canonical ensemble and its universal equivalence with the microcanonical ensemble, J. Stat. Phys. 119 (2005) 1283]. We show that this ensemble...

A special quantum-group oscillator presents an upper bound in its energy spectrum, which is preceded by an accumulation of infinite levels. The standard Boltzmann–Gibbs (BG) statistical-mechanics formalism is inadequate for dealing with such systems, since the partition function diverges for...

We show detailed calculations to obtain a metastable fluctuation–dissipation theorem (FDT) for Markovian systems with detailed balance. This is done by taking, for the metastable probability distribution, a superposition of the ground and the first excited state of the corresponding master...

We show numerically that the metastable autocorrelation of the magnetization in a bidimensional Ising model with Glauber dynamics follows a power law. In particular, we show that it has the form of a q-exponential for a wide set of parameters. This shows that the result is very robust. From this...

This paper is concerned with the stochastic generation of a large-scale galactic magnetic field and propagation of magnetic fronts in the subcritical regime. Starting with a two-component thin-disk αΩ-dynamo model in the axisymmetric case, we derive the equation for order parameter in the form...

We discuss the phase behaviour of spherical hard-core particles, with an attractive potential, as described by a hard-core Yukawa model. The ratio of the range of the attraction to the diameter of the particles is an important control parameter of the problem. Upon decreasing the range of the...

We show that a stochastic process on a complex plane can simulate decay from a metastable state. The simplest application of the method to a model in which the approach to equilibrium occurs through transitions over a potential barrier is discussed. The results are compared with direct numerical...