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

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 $\alpha \mathrm{\ne }0$. 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.