Helmholtz free energy confinement

Theoretically, several aspects of the Thommes-Findenegg experiment can be analyzed at the mean-field level [157]. A key quantity of a mean-field theory of confined fluids is the (Helmholtz) free energy, given by... 

Consider a one-component system of two phases confined to a cube of side, and hence of cross-section A = I. The two phases are separated by a horizontal surface, and the height z is measured from the mid-height of the vessel. The amount of substance n and the Helmholtz free energy F are given by... 

Secondly, in the theory of irreversible processes, variation principles may be expected to help establish a general statistical method for a system which is not far from equilibrium, just as the extremal property of entropy is quite important for establishing the statistical mechanics of matter in equilibrium. The distribution functions are determined so as to make thermod5mamic probability, the logarithm of which is the entropy, be a maximum under the imposed constraints. However, such methods for determining the statistical distribution of the s retem are confined to the case of a system in thermodynamic equilibrium. To deal with a system out of equilibrium, we must use a different device for each case, in contrast to the method of statistical thermodynamics, which is based on the general relation between the Helmholtz free energy and the partition function of the system. 

The other thermodynamic functions are also easily found. If we confine ourselves to low pressures, of the order of atmospheric pressure, we can neglect the term PV in the Gibbs free energy of liquid or solid. Then the Helmholtz and Gibbs free energies are approximately equal and are given by... 

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