Observational constraints on the product of dark energy chemical potential and number density in out-of-equilibrium models

Abstract: In this work, we impose observational limits on the product of dark energy chemical potential, $μ$, and number density, $n$, at the present time in out-of-equilibrium models, considering that particles can be created or destroyed in the fluid at a rate $Γ=3αH(a)$, where $α$ is a constant and $H(a)\equiv\dot{a}/a$ is the Hubble parameter. We combine the bounds derived from the positivity of entropy and the second law of thermodynamics with observational constraints on the Chevallier-Polarski-Linder (CPL) and Barboza-Alcaniz (BA) parameterizations of the equation of state (EoS) of the component. We use Type Ia supernovae (SN Ia) data from Pantheon+; baryon acoustic oscillation (BAO) data from DESI DR2; and cosmic microwave background (CMB) measurements from Planck. For $α>0$ (particle creation), the thermodynamic restrictions yield only upper limits for the $μ{0}n{0}$ product, while in the case of $α<0$ (particle destruction) they establish both upper and lower limits, allowing for a range of values to be obtained. In both scenarios, however, we find that the chemical potential of dark energy must be negative, $μ<0$, which indicates a preference for the phantom regime. In particular, when $α<0$, it is noted that the thermodynamic bounds are simultaneously compatible only for very small absolute values of $α$, with $α=-0.0002$ being the limiting case and resulting in $μ{0}n{0}(α=-0.0002)=-2.2_{-0.7}^{+1.0}\,\,GeV/m^{3}$.