The Φ-entropy: An information measure for non-Schrödinger type Hamiltonians

Abstract

In this paper, a new form of information measure was formulated and was named Φ-entropy which is of the form I(p_i) = ∑ p_i^Φ. This information measure needs to be differentiated first with its parameter Φ before limiting it to one to derive the Shannon entropy which makes it different to other information measures that needs only a limiting parameter to derive Shannon entropy. The validity of the Φ-entropy was also tested using the axiomatic conditions and a probability distribution was also derived which leads to systems with non-Schrödinger type Hamiltonians.