Abstract
In the present work, it is shown that the Maxwell relations can effectively be used to partially verify the thermodynamic consistency of the entropic lattice kinetic models. As an example, we consider the Constant Speed Kinetic Model (CSKM) which has recently been introduced in [J. Comp. Phys. 274, 803 (2014); Phys Rev. E 91, 063311 (2015)] and show that, for the quasi-equilibrium flows and at low Mach numbers, the entropy variations are proportional to the pressure variations. The entropy variations of the CSKM are logarithmic (given by the Burg entropy) while the pressure variations obey a nonlogarithmic equation of state. The proportionality of these variations, which is in accordance with the Maxwell relations, can be used to partially verify the thermodynamic consistency of the model. A similar treatment of the previously introduced entropic lattice kinetic models (e.g. of the conventional ELBM of [I. V. Karlin, A. Ferrante and H. C. Öttinger, Europhys. Lett. 47, 182 (1999)]), can provide a new ground for comparing the thermodynamic consistency of the existing entropic lattice kinetic models with each other.
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