A characterization of the segal entropy

We study the Segal entropy $\text{S(ψ∣τ) = -τ(}\text{dψ}\text{dτ}\text{ln}\text{dψ}\text{dτ}\text{)}$ of a normal state ψ on a W¹-algebra $\text{M}$ with respect to a faithful normal semi-finite trace τ on $\text{M}$ and we give a unique characterization of this general entropy concept by means of some natural properties.