Information theoretic extended entropy for steady heat condition

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Abstract
A phase space distribution for a far-from-equilibrium steady state in which thermodynamic temperature, T, and heat flux, J, are specified is calculated by maximising the information theoretic entropy. When this distribution is used to calculate free energy, F, the latter is obtained as a function of the distribution moduli which, in turn, are calculated from a consistency condition as functions of J and T. The coefficient of the O(J2) term in F can be expressed in terms of the radial distribution function, g2, and three-particle distribution, g3. A numerical estimate is made for a hard-sphere model of liquid Ar at 87 K and high density, using the Percus-Yevick solution for g2 and the Kirkwood superposition for g3. The estimate confirms the conclusion of an earlier theory that non-linear effects at liquid density are negligible except, possibly, for unrealistically large J. Fluctuation theory is invoked to make an estimate of the negligibly small O(J4) term in F.

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