# Derivation of density operators for generalized entropies with quantum analysis

## TL;DR

This paper presents a straightforward derivation of density operators for various generalized entropies using quantum analysis, highlighting its effectiveness in functional variation calculations involving trace operations.

## Contribution

It introduces a simple method to derive density operators for multiple entropies within quantum analysis, unifying the approach for both standard and generalized entropies.

## Key findings

- Derived density operators for Tsallis and Rényi entropies using quantum analysis.
- Derived density operators for Boltzmann-Gibbs and Burg entropies.
- Demonstrated the effectiveness of quantum analysis in entropy functional variations.

## Abstract

We gave a simple derivation of density operator with the quantum analysis. We dealt with the functional of a density operator, and applied maximum entropy principle. We obtained easily the density operators for the Tsallis entropy and R\'enyi entropy with the $q$-expectation value (escort average), and also obtained easily the density operators for the Boltzmann-Gibbs entropy and the Burg entropy with the conventional expectation value. The quantum analysis works effectively in the calculation of the variation of the functional which includes trace.