Characteristic state function

The characteristic state function or Massieu's potential^[1] in statistical mechanics refers to a particular relationship between the partition function of an ensemble.

In particular, if the partition function P satisfies

P=\exp(-\beta Q)\Leftrightarrow Q=-{\frac {1}{\beta }}\ln(P)

or

P=\exp(+\beta Q)\Leftrightarrow Q={\frac {1}{\beta }}\ln(P)

in which Q is a thermodynamic quantity, then Q is known as the "characteristic state function" of the ensemble corresponding to "P". Beta refers to the thermodynamic beta.

^ Balian, Roger (2017-11-01). "François Massieu and the thermodynamic potentials". Comptes Rendus Physique. 18 (9–10): 526–530. Bibcode:2017CRPhy..18..526B. doi:10.1016/j.crhy.2017.09.011. ISSN 1631-0705. "Massieu's potentials [...] are directly recovered as logarithms of partition functions."

[1] Balian, Roger (2017-11-01). "François Massieu and the thermodynamic potentials". Comptes Rendus Physique. 18 (9–10): 526–530. Bibcode:2017CRPhy..18..526B. doi:10.1016/j.crhy.2017.09.011. ISSN 1631-0705. "Massieu's potentials [...] are directly recovered as logarithms of partition functions."

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Characteristic state function

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