Laws and Statistical Mechanics

Statistical Inference and Statistical Mechanics

In this lecture, recent developments on connections between Markov processes and nonequilibrium statistical mechanical systems are discussed. A statistical mechanical analogy is developed for Markov processes and a local entropic measure of their true asymmetry is defined. Introducing partial observations, conditional and joint analogies are developed for Markov processes and their optimal filt...

Fractal Structures and Scaling Laws in the Universe. Statistical Mechanics of the Self-gravitating Gas

Fractal structures are observed in the universe in two very different ways. Firstly, in the gas forming the cold interstellar medium in scales from 10−4pc till 100pc. Secondly, the galaxy distribution has been observed to be fractal in scales up to hundreds of Mpc. We give here a short review of the statistical mechanical (and field theoretical) approach developed by us for the cold interstella...

Statistical Mechanics

Role of chaos for the validity of statistical mechanics laws: diffusion and conduction

Several years after the pioneering work by Fermi Pasta and Ulam, fundamental questions about the link between dynamical and statistical properties remain still open in modern statistical mechanics. Particularly controversial is the role of deterministic chaos for the validity and consistency of statistical approaches. This contribution reexamines such a debated issue taking inspiration from the...

Thermodynamics and Statistical Mechanics

The field of thermodynamics is easiest to understand in the context of Newtonian mechanics. Newtonian mechanics describes the effect of forces on objects. Thermodynamics describes the effect of heat transfer on objects. When heat is transferred,the temperature of an object changes.Temperature and heat are also intimately related to energy. A hot gas in a piston has a high pressure and it can do...