Deformed special relativity with an energy barrier of a minimum speed

Full text: This research aims to introduce a new principle of symmetry in the flat space-time by means of the elimination of the classical idea of rest, and by including a universal minimum limit of speed in the quantum world. Such a limit, unattainable by the particles, represents a preferred inertial reference frame associated with a universal background field that breaks Lorentz symmetry. So there emerges a new relativistic dynamics where a minimum speed forms an inferior energy barrier. One of the interesting implications of the existence of such a minimum speed is that it prevents the absolute zero temperature for an ultracold gas, according to the third law of thermodynamics. So we will be able to provide a fundamental dynamical explanation for the third law by means of a connection between such a phenomenological law and the new relativistic dynamics with a minimum speed. In other words we say that our relevant investigation is with respect to the problem of the absolute zero temperature in the thermodynamics of an ideal gas. We have made a connection between the 3 rd law of Thermodynamics and the new dynamics with a minimum speed by means of a relation between the absolute zero temperature (T = 0 deg K) and a minimum average speed (V) for a gas with N particles (molecules or atoms). Since T = 0 deg K is thermodynamically unattainable, we have shown this is due to the impossibility of reaching V from the new dynamics standpoint. (author)