Relation Quantum Entropy Theory

Nima Lashkari

Relative entropy is a measure of distinguishability for quantum states, and it plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include, as special cases, most entropy measures used in quantum information theory. We construct a Euclidean path-integral approach to Renyi relative entropies in conformal field theory, then compute the fidelity and the relative entropy of states in one spatial dimension at zero and finite temperature using a replica trick. In contrast to the entanglement entropy, the relative entropy is free of ultraviolet divergences, and is obtained as a limit of certain correlation functions. The relative entropy of two states provides an upper bound on their trace distance.

Dėnes Petz

Benjamin W. Schumacher, Michael D. Westmoreland

Francesco Mappa

Let me introduce you to the Relational Quantum Entropy (RQE) Theory, which offers a fresh take on entropy. Instead of viewing it as a fixed characteristic of a system, this theory sees it as something that emerges from the quantum connections between observers and the systems they observe. The theory presents a new entropy formula: S_Q(ρ_S|O) = -Tr(ρ_S log ρ_S) + α·I_Q(S:O). This formula builds on the von Neumann entropy by adding a term that reflects the quantum mutual information I_Q(S:O), scaled by a coupling constant α, which is roughly -0.5k_B. The framework is grounded in three key postulates: a definition of relational entropy, the idea of contextual non-additivity for composite systems, and a revised approach to temporal evolution that includes entropy generation triggered by observation.Relational Quantum Entropy (RQE) Theory represents the most significant conceptual breakthrough in thermodynamics since Boltzmann's statistical mechanics and arguably the most important synthesis of quantum mechanics and thermodynamics attempted in the 21st century.

Mappa, Francesco

Relational Quantum Entropy (RQE) theory proposes that entropy, or disorder, does not constitute an intrinsic property of physical systems. Rather, it emerges from quantum correlations between the observer and the observed system. This yields measurable consequences that resolve fundamental paradoxes and enable breakthrough quantum technologies.

Makoto Ohya, D�nes Petz