Towards a statistical mechanics of cities

Towards a Statistical Mechanics of Nonabelian Vortices

A detailed study is presented of classical field configurations describing nonabelian vortices in two spatial dimensions, when a global SO(3) symmetry is spontaneously broken to a discrete group IK isomorphic to the group of integers mod 4. The vortices in this model are characterized by the nonabelian fundamental group π1(SO(3)/IK) =Q8, which is isomorphic to the group of quaternions. We prese...

From Relativistic Mechanics towards Relativistic Statistical Mechanics

Till now, kinetic theory and statistical mechanics of either free or interacting point particles were well defined only in non-relativistic inertial frames in the absence of the long-range inertial forces present in accelerated frames. As shown in the introductory review at the relativistic level, only a relativistic kinetic theory of “world-lines” in inertial frames was known till recently due...

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...

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...