  A two parameter generalization of Boltzmann-Gibbs-Shannon entropy based on
natural logarithm is introduced. The generalization of the Shannon-Kinchinn
axioms corresponding to the two parameter entropy is proposed and verified. We
present the relative entropy, Jensen-Shannon divergence measure and check their
properties. The Fisher information measure, relative Fisher information and the
Jensen-Fisher information corresponding to this entropy are also derived. The
canonical distribution maximizing this entropy is derived and is found to be in
terms of the Lambert's W function. Also the Lesche stability and the
thermodynamic stability conditions are verified. Finally we propose a
generalization of a complexity measure and apply it to a two level system and a
system obeying exponential distribution. The results are compared with the
corresponding ones obtained using a similar measure based on the Shannon
entropy.
