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Rényi and von Neumann entropies of thermal state in Generalized Uncertainty Principle-corrected harmonic oscillator

The Rényi 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 $α$. While the von Neumann entropy with $α= 0$ 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 $α\neq 0$. The Rényi entropy $S_γ$ with nonzero $α$ also exhibits similar behavior at the large temperature region. In this region the Rényi entropy exhibit decreasing behavior with increasing the temperature. The decreasing rate becomes larger when the order of the Rényi entropy $γ$ is smaller.