According to the theory of Byers Brown, in a steady state detonation the entropy production between the shock and sonic locus is a maximum in a self-sustaining wave. This has shown to hold true for all one-dimensional cases. Byers Brown also suggested a novel variational approach by maximising the global entropy generation within the detonation driving zone to solve the problem of self-sustaining, two-dimensional steady curved detonation waves in a slab or cylindrical stick of explosive. Preliminary application of such a variational technique, albeit with simplifying assumptions, demonstrate its potential to provide a rapid and accurate solution method for the problem. In this paper, recent progress in the development and validation of the variational maximum entropy concept, for the case of weakly curved waves, are reported. The predictions of the theory are compared with those of Detonation Shock Dynamics theory.