Isolated and adiabatic susceptibilities

It is shown from quantum statistical calculations that the possible difference between isolated and adiabatic susceptibilities is due to a partial energy being conserved in a slowly increasing field. This energy is constructed using the unitary space of linear operators. The consequences for thermodynamics are discussed, and the isolated susceptibility is found to be exactly equal to the total adiabatic susceptibility as obtained from generalized thermodynamics (Fick and Schwegler) with two different temperatures.