Thermodynamic integration

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Thermodynamic integration is used to calculate the difference in the Helmholtz energy function, , between two states. The path must be continuous and reversible, i.e., the system must evolve through a succession of equilibrium states (Ref. 1 Eq. 3.5)

Isothermal integration[edit]

At constant temperature (Ref. 2 Eq. 5):

Isobaric integration[edit]

At constant pressure (Ref. 2 Eq. 6):

where is the Gibbs energy function and is the enthalpy.

Isochoric integration[edit]

At constant volume (Ref. 2 Eq. 7):

where is the internal energy.

See also[edit]


  1. J. A. Barker and D. Henderson "What is "liquid"? Understanding the states of matter ", Reviews of Modern Physics 48 pp. 587 - 671 (1976)
  2. C. Vega, E. Sanz, J. L. F. Abascal and E. G. Noya "Determination of phase diagrams via computer simulation: methodology and applications to water, electrolytes and proteins", Journal of Physics: Condensed Matter 20 153101 (2008) (section 4)

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