Abstract. General classical arguments on the time evolution of the phase-space density can be used to derive constraints on the mass of particle candidates for the cosmological dark matter (DM). The resulting Tremaine-Gunn limit is extremely useful in constraining particle DM models. In certain models, however, the DM particle mass varies appreciably over time. In this work, we generalize the phase-space limits on possible DM particle masses to these scenarios. We then examine the ensuing cosmological implications on the effective DM equation of state and indirect DM detection.