Casimir Coefficients and Minimum Entropy Production

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Abstract
The rate equations obeyed by scalar relaxation parameters in a liquid are extended to include inertial terms in the form of second-order time derivatives, and the relations containing these terms are then written formally as first-order equations by treating first-order time derivatives as additional parameters. The resulting equations are interpreted thermodynamically as phenomenological relations containing anti-symmetric Casimir coefficients, and this interpretation leads, with application of the Onsager-Casimir reciprocity theorem, to an additional set of phenomenological equations which reduces to those used in an earlier relaxation theory when inertial effects are neglected. In this way, earlier formulas for the bulk viscosity and high-frequency bulk modulus are recovered unchanged. It is also shown why Prigogine's minimum entropy production theorem should no longer hold when one considers inertial effects.