Statistical Mechanics (McQuarrie, Donald A.)

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 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...

Gravitational Statistical Mechanics: a Model

Using the quantum Hamiltonian for a gravitational system with boundary, we find the partition function and derive the resulting thermody-namics. The Hamiltonian, and starting point for this calculation, is the boundary term required by functional differentiability of the action for Lorentzian general relativity. In this model, states of quantum geometry are represented by spin networks. We show...

A Study of Na/K Feldspar Solid Solution Using Statistical Mechanics

Thermal behavior of various solid feldspars are different, namely those of bivalent cations show no change in the distribution of Al and Si atoms, whereas feldspars of univalent cations become more disordered with raising temperature. In the latter case Al atoms migrate from the sites they occupe at low temperatures and interchange positions with the Si atoms. At high temperatures (but stil...