Entropic confinement in an Extended Uncertainty Principle (EUP)-deformed phase space

Abstract

We investigate the Extended Uncertainty Principle (EUP) from the perspective of phase-space structure and statistical mechanics. Starting from the deformed Poisson algebra, we derive the corresponding modification of the D-dimensional phase-space measure. This deformation induces a position-dependent weighting of configurations, which can be interpreted as an entropy-like contribution associated with the local density of accessible microstates. The resulting entropy gradient generates an attractive entropic force that diverges at a finite radius, providing a mechanism for confinement without an external potential, with the maximal length scale emerging as a natural boundary of the system.