  We study the dynamical consequences of Maggiore's unique generalised
uncertainty principle (GUP). We find that it leads naturally, and generically,
to novel consequences. In the high temperature limit, there is a drastic
reduction in the degrees of freedom, of the type found, for example, in strings
far above the Hagedorn temperature. In view of this, the present GUP may
perhaps be taken as the new version of the Heisenberg uncertainty principle,
conjectured by Atick and Witten to be responsible for such reduction. Also, the
present GUP leads naturally to varying speed of light and modified dispersion
relations. They are likely to have novel implications for cosmology and black
hole physics, a few of which we discuss qualitatively.

High Energy Physics - Theory;Astrophysics;Condensed Matter;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology;Quantum Physics