Physics II

The concept of entropy connects the number of possible configurations with the number of variables in large stochastic systems. Independent or weakly interacting variables render the number of configurations scale exponentially with the number of variables, making the Boltzmann–Gibbs–Shannon entropy extensive. In systems with strongly interacting variables, or with variables driven by history-dependent dynamics, this is no longer true.

In turbulent flows energy cascades from larger to smaller scales following the Kolmogorov -5/3 power law. An analytical picture of the process underlying cascades in fluids or in other systems is not known. Based on a well-known discrete map we show a procedure that generates an analytical structure that produces a cascade from which the energy scaling law for isotropic homogeneous turbulence can be calculated. It is done by finding a function that unveils a non-self-similar (possibly) multifractal ruling the cascade.

Loop-erased random walks, charge-density waves at depinning, the Abelian sandpile model and phi^4 theory with n=-2 components are a priori very different systems. We link all these models together with a common theory.

Roughness of vicinal surface is studied by calculating surface width using the Monte Carlo Method in the non-equilibrium steady state in order to clarify discrepancies between theoretical results and experiments. The adopted model is a restricted solid-on-solid (RSOS) model with a discrete Hamiltonian. Here, “restricted” means that the surface-height difference between nearest-neighbor sites is restricted to 0, and ±1.