Gibbs free energy insertion thermodynamics

As in the classical domain, quantum thermal properties are more involved to evaluate. In the canonical ensemble the central quantity is Helmholtz free energy A, from which Gibbs free energy and entropy are straightforward to obtain by making use of E and p. The standard methods to fix thermal properties are thermodynamic integration [22, 23] with respect to a parameter f, and Widom particle insertion method [236]. Thermodynamic integration for Helmholtz A relies on the identity... 

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