Characteristic state function
The characteristic state function or Massieu's potential 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 ( − β Q ) ⇔ Q = − 1 β ln ( P ) {\displaystyle P=\exp(-\beta Q)\Leftrightarrow Q=-{\frac {1}{\beta }}\ln(P)} or P = exp ( + β Q ) ⇔ Q = 1 β ln ( P ) {\displaystyle 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.
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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
- or
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.
Examples
[edit]- The microcanonical ensemble satisfies hence, its characteristic state function is .
- The canonical ensemble satisfies hence, its characteristic state function is the Helmholtz free energy .
- The grand canonical ensemble satisfies , so its characteristic state function is the Grand potential .
- The isothermal-isobaric ensemble satisfies so its characteristic function is the Gibbs free energy .
State functions are those which tell about the equilibrium state of a system
References
[edit]- ^ 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."