Bounds for the Isothermal, Adiabatic, and Isolated Static Susceptibility Tensors

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Abstract
Quantum-statistical proofs are given that the isolated (or Kubo) susceptibility tensor is positive indefinite and is bounded from above by the adiabatic susceptibility tensor, while the isothermal susceptibility tensor is positive definite and is bounded from below by the adiabatic susceptibility tensor. The results apply to either the static dielectric or magnetic cases. Biasing fields and permanent dipole moments may be present if desired. Criteria for equality of the various susceptibilities are established. Contact is made with work of Falk, Caspers, Mountain, Klein, Rosenfeld, and Saitô.