2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/25684We show that thermalization of the motion of atoms at negative temperature is possible in an optical lattice, for conditions that are feasible in current experiments. We present a method for reversibly inverting the temperature of a trapped gas. Moreover, a negative-temperature ensemble can be cooled, reducing abs(T), by evaporation of the lowest-energy particles. This enables the attainment of the Bose-Einstein condensation phase transition at negative temperature.4 pages 5 figures; v4: Typo corrections. Accepted Phys. Rev. LettStatistical Mechanicstext