Statistical mechanics of galaxies

Statistical Mechanics

Statistical Mechanics

where pi ≡ p(x = i). If only M of the K states have non-zero probability and that probability is 1/M then S = logM . In this special case the entropy is the log of the number of occupied states. An analog of this special case in the continuous domain occurs in Liouville’s Theorem. This states that if the volume of phase space (i.e. of the x variable, but now multivariate and continuous) is some...

Statistical mechanics of networks.

We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the same role in the study of networks as is played by the Boltzmann distribution in classical statistical mechanics; they offer the best prediction of network p...

Statistical mechanics of money

In a closed economic system, money is conserved. Thus, by analogy with energy, the equilibrium probability distribution of money must follow the exponential Boltzmann-Gibbs law characterized by an effective temperature equal to the average amount of money per economic agent. We demonstrate how the Boltzmann-Gibbs distribution emerges in computer simulations of economic models. Then we consider ...

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...