The two-sided Bogoliubov inequality for relative free energies, previously proved for quantum-mechanical systems, is extended to arbitrary von Neumann algebras, alongside new Hilbert-space-level monotonicity inequalities for the Araki-Uhlmann relative entropy.
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Monotonicity of the Relative Entropy and the Two-sided Bogoliubov Inequality in von Neumann Algebras
The two-sided Bogoliubov inequality for relative free energies, previously proved for quantum-mechanical systems, is extended to arbitrary von Neumann algebras, alongside new Hilbert-space-level monotonicity inequalities for the Araki-Uhlmann relative entropy.