Note on Von Neumann Entropy and the Ordering of Inverse Temperatures

• URL: http://arxiv.org/abs/2503.18953v1
• Date: Thu, 13 Mar 2025 05:39:55 GMT
• Title: Note on Von Neumann Entropy and the Ordering of Inverse Temperatures
• Authors: Rohit Kishan Ray,
• Abstract summary: von Neumann entropy is a monotonically increasing function of temperature.<n>rho_beta$ for a given Hamiltonian $H$ satisfies $S(rho_beta) geq S(rho_beta) iff beta_1 leq beta_2$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: I show that for two inverse temperatures $\beta_1$ and $\beta_2$, the von Neumann entropy $S(\rho_\beta)$ of the Gibbs state $\rho_\beta$ for a given Hamiltonian $H$ satisfies $S(\rho_{\beta_1}) \geq S(\rho_{\beta_2}) \iff \beta_{1} \leq \beta_{2}$. That is, von Neumann entropy is a monotonically increasing function of temperature.

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