Abstract
It has been conjectured in the literature that for the Boltzmann equation: (i) Boltzmann's H has the property of possessing successive (semi-) definite time derivatives with alternating sign, (ii) this property is suitable for selecting H from further possibly existing (Lyapunov) functions with (semi-) definite first time derivative. The authors show at first that, in contradiction to (ii), for Maxwell's model of a discrete velocity gas the corresponding variant of H is not the unique Lyapunov function having the property (i) and suitable to define a 'non-equilibrium entropy' with respect to the (spatially homogeneous) Boltzmann equation of this model. Secondly, in the case of the complete spatially inhomogeneous Boltzmann equation, H is generally not (semi-)definite in contradiction to the above-mentioned conjecture (i).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
