On a nonlinear recurrent relation

We study the limiting behavior for the solutions of a nonlinear recurrent relation which arises from the study of Navier-Stokes equations. Some stability theorems are also shown concerning a related class of linear recurrent relations.Comment: to appear in Journal of Statistical Physic

Exact formula for currents in strongly pumped diffusive systems

We analyze a generic model of mesoscopic machines driven by the nonadiabatic variation of external parameters. We derive a formula for the probability current; as a consequence we obtain a no-pumping theorem for cyclic processes satisfying detailed balance and demonstrate that the rectification of current requires broken spatial symmetry.Comment: 10 pages, accepted for publication in the Journal of Statistical Physic

The analyticity region of the hard sphere gas. Improved bounds

We find an improved estimate of the radius of analyticity of the pressure of the hard-sphere gas in $d$ dimensions. The estimates are determined by the volume of multidimensional regions that can be numerically computed. For $d=2$, for instance, our estimate is about 40% larger than the classical one.Comment: 4 pages, to appear in Journal of Statistical Physic

Russo's formula for random interlacements

In this paper we obtain a couple of explicit expressions for the derivative of the probability of an increasing event in the random interlacements model. The event is supported in a finite subset of the lattice, and the derivative is with respect to the intensity parameter of the model.Comment: 14 pages, 3 figures, added section, accepted for publication in the Journal of Statistical Physic

Entropy and Time

The emergence of a direction of time in statistical mechanics from an underlying time-reversal-invariant dynamics is explained by examining a simple model. The manner in which time-reversal symmetry is preserved and the role of initial conditions are emphasized. An extension of the model to finite temperatures is also discussed.Comment: 9 pages, 8eps figures. To appear in the theme issue of the American Journal of Physics on Statistical Physic