Progress in the Understanding of the Fluctuating Lattice Boltzmann   Equation
  We give a brief account of the development of methods to include thermal fluctuations into lattice Boltzmann algorithms. Emphasis is put on our recent work (Phys. Rev. E 76, 036704 (2007)) which provides a clear understanding in terms of statistical mechanics. 
Burkhard Duenweg, Ulf D. Schiller, Anthony J. C. Ladd