Alternative Views on Entropy Models and Statistical Approaches in Extended Thermodynamics

Abstract

Three formalisms are considered which challenge extended irreversible thermodynamics (EIT) or derivations thereof. One of these argues that we can control heat flow along a rigid conductor to make internal energy U depend only on temperature T in disagreement with EIT. However, such a process is forbidden in general by an exact equation for second challenge argues that the Boltzmann entropy must be used in a dilute gas, equivalent to EIT with an infinity of variables, and that the Liouville equation cannot describe irreversibility. However, Robertson has shown the Liouville equation to be consistent with irreversible linear heat conduction. Luzzi and Vasconcellos derive EIT approximately from a modified Liouville equation. The Robertson formalism provides a tractable approach without their approximations.