Related papers: The Entropy Region is not Closed Under Duality
We investigate the transformation of entanglement entropy under dualities, using the Kramers-Wannier duality present in the transverse field Ising model as our example. Entanglement entropy between local spin degrees of freedom is not…
A 1972 duality conjecture due to Pietsch asserts that the entropy numbers of a compact operator acting between two Banach spaces and those of its adjoint are (in an appropriate sense) equivalent. This is equivalent to a dimension free…
The entropy of a closure operator has been recently proposed for the study of network coding and secret sharing. In this paper, we study closure operators in relation to their entropy. We first introduce four different kinds of rank…
We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no…
We use rigorous non-equilibrium thermodynamic arguments to prove (i) the residual entropy of any system is bounded below by the experimentally (calorimetrically) determined absolute temperature entropy, which itself is bounded below by the…
Qubit Models which aim to resolve the information paradox must not redefine entanglement entropy as a redefinition does not address the correct issue of the information paradox. The purpose of this letter is to understand why any…
We develop a duality for operations on nested pairs of modules that generalizes the duality between absolute interior operations and residual closure operations from [ER21], extending our previous results to the expanded context. We apply…
The analysis of the entanglement entropy of a subsystem of a one-dimensional quantum system is a powerful tool for unravelling its critical nature. For instance, the scaling behaviour of the entanglement entropy determines the central…
In holographic duality, boundary states that have semiclassical bulk duals must obey inequalities, which bound their subsystems' von Neumann entropies. Hitherto known inequalities constrain entropies of reduced states on up to $N=5$…
Given a manifold $\mathcal{M} \subset \mathbb{R}^n$, we consider all codimension-1 submanifolds of $\mathcal{M}$ that satisfy the generalized Stokes' theorem and show that $\partial\mathcal{M}$ uniquely maximizes the associated entropy…
We report on some general results on the physics of extremal BPS black holes in four and five dimensions. The duality-invariant entropy-formula for all $N>2$ extended supergravities is derived. Its relation with the fixed-scalar condition…
We study the Euler numbers and the entropies of the non-extremal intersecting D-branes in ten-dimensions. We use the surface gravity to constrain the compactification radii. We correctly obtain the integer valued Euler numbers for these…
Certain duality of relative entropy can fail for chiral conformal net with nontrivial representations. In this paper we quantify such statement by defining a quantity which measures the failure of such duality, and identify this quantity…
The frequent misunderstanding of information entropy is pointed out. It is shown that, contrary to fortuitous situations and common beliefs, there is no general interrelation between the information entropy and the thermodynamical entropy.…
The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes…
The aim of this work is to verify the new entropic and information inequalities for non-composite systems using experimental $5 \times 5$ density matrix of the qudit state, measured by the tomographic method in a multi-level superconducting…
We present an extension of the duality theorem, previously defined by S. Catani et al. on the one-loop level, to higher loop orders. The duality theorem provides a relation between loop integrals and tree-level phase-space integrals. Here,…
We show that nonabelian duality is not a symmetry of a conformal field theory, but rather a symmetry between different theories. We expose a nonlocal symmetry of nonabelian dual theories. We show how, in the case with vanishing isotropy, it…
The monotonicity of entropy is investigated for real quadratic rational maps on the real circle $\mathbb{R}\cup\{\infty\}$ based on the natural partition of the corresponding moduli space $\mathcal{M}_2(\mathbb{R})$ into its monotonic,…
In this paper, we analyze the relationship between entropy and information in the context of the mixing process of two identical ideal gases. We will argue that entropy has a special information-based feature that is enfolded in the…