https://doi.org/10.1140/epjp/s13360-020-00472-y
Regular Article
Observers and relative entropy of G-sets
Department of Mathematics, Faculty of Science, University of Jiroft, 78671-61167, Jiroft, Iran
Received:
6
August
2019
Accepted:
19
May
2020
Published online:
13
June
2020
In the current study, a new type of relative entropy is presented through observable objects in quantum mechanics as the probability measures. The relative probability measures as an extension of probability measures are considered via one-dimensional observers. The notion of relative entropy of the semigroup on a relative measure space is introduced using the mathematical modeling of an observable object. Moreover, it is proved that this nonnegative quantity is invariant under 
-isomorphism. Finally, we applied this concept to specific semigroups to extract Kolmogorov entropy of a dynamical system as a special case.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
