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Note on Von Neumann Entropy and the Ordering of Inverse Temperatures

Rohit Kishan Ray

Abstract

I show that for two inverse temperatures $β_1$ and $β_2$, the von Neumann entropy $S(ρ_β)$ of the Gibbs state $ρ_β$ for a given Hamiltonian $H$ satisfies $S(ρ_{β_1}) \geq S(ρ_{β_2}) \iff β_{1} \leq β_{2}$. That is, von Neumann entropy is a monotonically increasing function of temperature.

Note on Von Neumann Entropy and the Ordering of Inverse Temperatures

Abstract

I show that for two inverse temperatures and , the von Neumann entropy of the Gibbs state for a given Hamiltonian satisfies . That is, von Neumann entropy is a monotonically increasing function of temperature.

Paper Structure

This paper contains 2 theorems, 22 equations.

Key Result

Lemma 1

If the for all positive reals $p_i,q_i$, $i=1(1)N$ we have the following relation: then it implies,

Theorems & Definitions (2)

  • Lemma 1
  • Theorem 1