This research aims to introduce a new principle in the flat space-time geometry through the elimination of the classical idea of rest and by including a universal minimum limit of speed in the quantum world. This limit, unattainable by the particles, represents a preferred inertial reference frame associated with a universal background field that breaks Lorentz symmetry. There emerges a new relativistic dynamics where a minimum speed forms an inferior energy barrier. One of the interesting consequences 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 through a connection between such a phenomenological law and the new relativistic dynamics with a minimum speed.
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