Renyi 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 $alpha eq 0$. 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.