# Behavior of Shannon entropy around an exceptional point in an open microcavity

## TL;DR

This study explores how Shannon entropy behaves near an exceptional point in an open microcavity, revealing extremal values, discontinuities, and a complex topological structure in the entropy landscape.

## Contribution

It provides the first analysis of Shannon entropy behavior around an exceptional point in a non-Hermitian microcavity system.

## Key findings

- Shannon entropy reaches an extremum at the exceptional point.
- Discontinuities in Shannon entropy occur across specific parameter lines.
- The entropy surfaces exhibit a nontrivial topological structure.

## Abstract

We have investigated the Shannon entropy around an exceptional point (EP) in an open elliptical microcavity as a non-Hermitian system. The Shannon entropy had an extreme value at the EP in the parameter space. The Shannon entropies showed discontinuity across a specific line in the parameter space, directly related to the occurrence of exchange of the Shannon entropy as well as the mode patterns with that line as a boundary. This feature results in a nontrivial topological structure of the Shannon entropy surfaces.