UNIVERSAL JUMP IN SLOPE OF THE CHEMICAL-POTENTIAL AT 2ND-ORDER PHASE-TRANSITIONS

We point out that in systems exhibiting a second-order phase transition, the chemical potential has a jump in slope at the critical temperature, provided that T(c) depends on particle density. We derive a generally valid thermodynamic relation between the specific heat jump, the jump in dmu/dT, and dlnT(c)/dn, with mu the chemical potential and n the density of the particles causing the transition. This relation is similar, but not equivalent, to the more familiar Ehrenfest relation between expansivity, specific heat, and dlnT(c)/dp, with p the externally applied pressure.