Related papers: Modular energy inequalities from relative entropy
We derive the expressions for canonical energy, momentum, and angular momentum for multiple metric theories. We prove that although the metric fields are generally interacting, the total energy is the sum of conserved energies corresponding…
We prove a lower bound on the relative entropy between two finite-dimensional states in terms of their entropy difference and the dimension of the underlying space. The inequality is tight in the sense that equality can be attained for any…
Using the electrostatic potential $u$ due to a uniformly charged body $\Omega\subset\mathbb R^n$, $n\geq 3$, we introduce a family of monotone quantities associated with the level set flow of $u$. The derived monotonicity formulas are…
We study relative entropy in QFT, comparing the vacuum state to a special family of purifications determined by an input state and constructed using relative modular flow. We use this to prove a conjecture by Wall that relates the shape…
Building on the "quantum inequalities" introduced by Ford, I argue that the negative local energies encountered in quantum field theory can only be observed by detectors with positive energies at least as great in magnitude. This means that…
We begin to investigate the question of what modifications in energy-momentum tensor can yield correct MOND regime. As a starting study, we refrain from insisting on an action principle and focus exclusively on the equations of motion. The…
For a general dark-energy equation of state, we estimate the maximum possible radius of massive structures that are not destabilized by the acceleration of the cosmological expansion. A comparison with known stable structures constrains the…
A criterion of local continuity of the relative entropy of resource -- the relative entropy distance to the set of free states -- is obtained. Several basic corollaries of this criterion are presented. Applications to the relative entropy…
Density functional theory can be extended to excited states by means of a unified variational approach for passive state ensembles. This extension overcomes the restriction of the typical density functional approach to ground states, and…
A completely new approach to the problem of energy distribution in statistical mechanics is developed that results in a general, combinatorial formula for the density of states. Relying on the approach the energy equipartition principle is…
It is well known that there can be negative energy densities in quantum field theory. Most of the work done in this area has involved free non-interacting systems. In this paper we show how a quantum state with negative energy density can…
We identify new universal properties of the energy eigenstates of chaotic systems with local interactions, which distinguish them both from integrable systems and from non-local chaotic systems. We study the relation between the energy…
The standard assumption for the equilibrium microcanonical state in quantum mechanics, that the system must be in one of the energy eigenstates, is weakened so as to allow superpositions of states. The weakened form of the microcanonical…
The regularized vacuum energy (or energy density) of a quantum field subjected to static external conditions is shown to satisfy a certain partial differential equation with respect to two variables, the mass and the "time" (ultraviolet…
We apply concepts from the quantum measurement theory to obtain some cosmological neutrino background (C$\nu$B) properties and discuss their relevance in defining theoretical bounds on cosmological neutrino energy density. Describing three…
Using a one-dimensional macromolecule in aqueous solution as an illustration, we demonstrate that the relative entropy from information theory, $\sum_k p_k\ln(p_k/p_k^*)$, has a natural role in the energetics of equilibrium and…
The concept of energy lies at the foundation of physical science. In general relativity and quantum field theory, the positivity and conservation of energy are encapsulated by the so-called energy-momentum tensor and the energy conditions.…
The study of conditional $q$-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The $q$-entropies depend on the density matrix $\rho$…
The novel concept of quantum logical entropy is presented and analyzed. We prove several basic properties of this entropy with regard to density matrices. We hereby motivate a different approach for the assignment of quantum entropy to…
Inspired by Verlinde's idea, some modified versions of entropic gravity have appeared in the literature. Extending them in a unified formalism, we derive the generalized gravitational equations accordingly. From gravitational equations, the…