R\'enyi and von Neumann entropies of thermal state in Generalized Uncertainty Principle-corrected harmonic oscillator

TL;DR

This paper calculates the Rényi and von Neumann entropies of a GUP-corrected harmonic oscillator's thermal state, revealing temperature-dependent behaviors altered by the GUP parameter, including entropy maximization at finite temperature.

Contribution

It provides explicit first-order calculations of entropies in a GUP-modified harmonic oscillator, highlighting novel temperature-dependent entropy behaviors due to GUP effects.

Findings

Von Neumann entropy peaks at finite temperature when GUP parameter is nonzero.

GUP modifies the temperature dependence of entropies, causing decreasing behavior at high temperatures.

Rényi entropy's decreasing rate at high temperature depends on its order gamma.

Abstract

The R\'{e}nyi and von Neumann entropies of the thermal state in the generalized uncertainty principle (GUP)-corrected single harmonic oscillator system are explicitly computed within the first order of the GUP parameter $\alpha$. While the von Neumann entropy with $\alpha = 0$ exhibits a monotonically increasing behavior in external temperature, the nonzero GUP parameter makes the decreasing behavior of the von Neumann entropy at the large temperature region. As a result, the von Neumann entropy is maximized at the finite temperature if $\alpha \neq 0$. The R\'{e}nyi entropy $S_{\gamma}$ with nonzero $\alpha$ also exhibits similar behavior at the large temperature region. In this region the R\'{e}nyi entropy exhibit decreasing behavior with increasing the temperature. The decreasing rate becomes larger when the order of the R\'{e}nyi entropy $\gamma$ is smaller.