2025/01/07 by Stefan Hollands, Roberto Longo, Hollands, Stefan +1 · 2 citations
Chemistry · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum and electron transport phenomena
paper · pdf · doi:10.48550/arxiv.2501.03849
openalex publication_date 2025/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We generalize the energy-entropy ratio inequality in quantum field theory (QFT) established by one of us from localized states to a larger class of states. The states considered in this paper can be in a charged (non-vacuum) representation of the QFT or may be only approximately localized in the region under consideration. Our inequality is S(Ψ| | Ω) ≤ 2πR ( Ψ, HρΨ) + log d(ρ) + ε, where S is the relative entropy, where R is a "radius" (width) characterizing the size of the region, d(ρ) is the statistical (quantum) dimension of the given charged sector ρ hosting the quantum state Ψ, Ω is the vacuum state, Hρ is the Hamiltonian in the charged sector, and ε is a tolerance measuring the deviation of Ψ from the vacuum according to observers in the causal complement of the region.