Method of the solution of the main problem of homogeneous spaces thermodynamics on non-compact spaces in the case of non-compact homogeneous spaces is presented in the article. The method is based on the formalism of coadjoint orbits. In that article we present algorithm that allows e ciently evaluate heat kernel on non-compact homogeneous spaces. The method is illustrated with non-trivial exam...

It is well known that no infinite homogeneous space is both compact and extremally disconnected. (Since there are infinite compact homogeneous spaces and infinite extremally disconnected homogeneous spaces, it is the combination of compactness and extremal disconnectedness that brings about this result.) The following question then arises naturally: How “close to compact” can a homogeneous, ext...