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Thermodynamic Pressure


Thermodynamic pressure is the logarithm of a statistical-mechanical partition function divided by the system size. For N spins with reference measure nu_N and energy H_N, the convention is

 p_N=1/Nlninte^(-betaH_N(sigma))dnu_N(sigma).

Its limit as N->infty, when it exists, is the infinite-system pressure. The physical free energy per spin in this convention is -p_N/beta. For uniform probability on binary spins, p_N=0 at zero interaction, whereas counting measure gives p_N=ln2.

In a disordered system, quenched pressure averages lnZ_N over the disorder, while annealed pressure uses lnEZ_N. These operations generally differ.


See also

Annealed Law, Canonical Free Energy, Gibbs Measure, Pair Potential, Quenched Law

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References

Friedli, S. and Velenik, Y. Statistical Mechanics of Lattice Systems: A Concrete Mathematical Introduction. Cambridge, England: Cambridge University Press, 2017. https://doi.org/10.1017/9781316882603.

Cite this as:

Weisstein, Eric W. "Thermodynamic Pressure." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ThermodynamicPressure.html

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