Test of Information Theory on the Boltzmann Equation
  We examine information theory using the steady-state Boltzmann equation. In a nonequilibrium steady-state system under steady heat conduction, the thermodynamic quantities from information theory are calculated and compared with those from the steady-state Boltzmann equation. We have found that information theory is inconsistent with the steady-state Boltzmann equation. 
Kim Hyeon-Deuk and Hisao Hayakawa