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arXiv · 2006.02717

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

MuSeong Kim·Mi-Ra Hwang·Eylee Jung·DaeKil Park
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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.

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MuSeong Kim, Mi-Ra Hwang, Eylee Jung, DaeKil Park. 2020-06-04. R\'enyi and von Neumann entropies of thermal state in Generalized Uncertainty Principle-corrected harmonic oscillator. https://doi.org/10.1142/s0217732321502503

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