Smoluchowski and Fokker–Planck equations for the stochastic dynamics of order parameters have been derived previously. The question of the validity of the truncated perturbation series and the initial data for which these equations exist remains unexplored. To address these questions, we take...

Recently, Kleidon suggested a restatement of the Gaia hypothesis based on Maximum Entropy approaches to the Earth system. Refuting conceptions of Gaia as a homeostatic system, Gaia is seen as a non-equilibrium thermodynamic system which continuously moves away from equilibrium, driven by maximum...

The entropy approach to the evolution of open systems is analyzed, using Lotka’s principle as a starting point. A Lagrangian is sought after to develop an analytical method for the evaluation of the stationary states of open irreversible systems. The stationary conditions for open systems are...

We re-examine a two-dimensional forest-fire model via Monte-Carlo simulations and show the existence of two length scales with different critical exponents associated with clusters and with the usual two-point correlation function of trees. We check resp. improve previously obtained values for...

Certain systems with slow driving and avalanche-like dissipation events are naturally close to a critical point when the ratio of two energy scales is large. The first energy scale is the threshold above which an avalanche is triggered, the second scale is the threshold above which a site is...

Anomalous large thermal conductivity has been observed numerically and experimentally in one and two dimensional systems. All explicitly solvable microscopic models proposed to date did not explain this phenomenon and there is an open debate about the role of conservation of momentum. We...

Recently, Kleidon suggested a restatement of the Gaia hypothesis based on Maximum Entropy approaches to the Earth system. Refuting conceptions of Gaia as a homeostatic system, Gaia is seen as a non-equilibrium thermodynamic system which continuously moves away from equilibrium, driven by maximum...

We compare three simple models that reproduce qualitatively the emergent swarming behavior of bird flocks, fish schools, and other groups of self-propelled agents by using a new set of diagnosis tools related to the agents’ spatial distribution. Two of these correspond in fact to different...

The extremum complexity momentum distribution for an isolated monodimensional ideal gas out of equilibrium is analytically approximated. In a first approximation, it consists of a double non-overlapping Gaussian distribution. In good agreement with this result, the numerical simulations of a...

The most general aim of "Investigations" is to explore whether there might, conceivably, be some general laws governing a certain class of non-equilibrium systems - namely the class of coevolutionary self-constructing communities of autonomous agents. The first lecture discusses the general...