The coexistence of ordered and chaotic dynamics in one and the same system has been detected already several years ago. A thorough description of a complex dynamical system, both from a mechanical and from a statistical point of view, requires the determination of the level of order and...

The lecture notes give an introduction to some aspects of fluctuations in driven systems. First, a particularly straightforward derivation of fluctuation theorems and their relation to linear response will be given. Being particularly simple the derivation gives clear limitations on the regime...

We propose a general framework to study the stability of the subspace spanned by P consecutive eigenvectors of a generic symmetric matrix H0 when a small perturbation is added. This problem is relevant in various contexts, including quantum dissipation (H0 is then the Hamiltonian) and financial...

The equilibrium statistical mechanics of the energy-enstrophy theory for the barotropic vorticity equation is solved exactly in the sense that a explicitly nonGaussian configurational integral is calculated in closed form. A family of lattice vortex gas models for the barotropic vorticity...

We address the issue of generalizing the thermodynamic quantities via q-deformation, i.e., via the q-algebra that describes q-bosons and q-fermions. In this study with the application of q-deformation to the Landau diamagnetism problem in two dimensions, embedded in a D-dimensional space, we...

This study introduces the constrained forms of the Shannon information entropy and Kullback–Leibler cross-entropy functions. Applicable to a closed system, these functions incorporate the constraints on the system in a generic fashion, irrespective of the form or even the number of the...

By seeking to uncover the rules of collective human activities, today's statistical physicists are aiming to return to their roots. Statistics originated in the study of social numbers in the 17th century, and the discovery of statistical invariants in data on births and deaths, crimes and...

The thermodynamics of the unitary (normalized spin) quantum and classical Ising models with skew magnetic field, for |J|β≲0.9, is derived for the ferromagnetic and antiferromagnetic cases. The high-temperature expansion (β-expansion) of the Helmholtz free energy is calculated up to order β7...

We investigate the lifetime distribution P(τ,t) in one and two dimensional coarsening processes modelled by Ising–Glauber dynamics at zero temperature. The lifetime τ is defined as the time that elapses between two successive flips in the time interval (0,t) or between the last flip and the...

Thermodynamical properties of spin-S Ising chains can nowadays be easily obtained using numerical calculation. However, from a mathematical point of view, its exact solution for arbitrary spin is still a challenge. Only limiting cases have been solved exactly, such as the infinite spin limit and...