The uncertainty measure for q-exponential distribution function

Based on the q-exponential distribution which has been observed in more and more physical systems, the uncertainty measure of such an abnormal distribution can be derived by employing a variational relationship which can be traced from the first and se- cond thermodynamic laws. The uncertainty measure obtained here can be considered as the entropic form for the abnormal physi- cal systems having observable q-exponential distribution. This entropy will tend to the Boltzmann-Gibbs entropy when the non- extensive parameter tends to unity. It is very important to find that this entropic form is always concave and the systemic entropy is maximizable.