An information measure leading to highest energy state as the most probable state

Abstract

Many systems cannot be described by the standard entropy such as the Shannon entropy. Entropy can be generalised to accomodate this insufficiency. In this paper, we have chosen the information measure to be I = Σ_i p_i^3/2. This information measure satisfies the conditions for generalized entropy such as the Khinchin axioms. The statistical mechanics was derived and it leads to a phenomenon where the system has a bounded energy and the most probable state is the highest energy. Moreover, it is found that for a system having an energy spectrum that depends linearly on a single parameter the system is at absolute infinite temperature even when its energy is finite.