Related papers: Why would multiplicities be log-concave ?
A short and elementary proof of the joint convexity of relative entropy is presented, using nothing beyond linear algebra. The key ingredients are an easily verified integral representation and the strategy used to prove the Cauchy-Schwarz…
Entropy is a concept that has traditionally been reliant on a definite notion of causality. However, without a definite notion of causality, the concept of entropy is not all lost. Indefinite causal structure results from combining…
Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…
We give a simple proof of a strengthened version of a theorem of Lieb that played a key role in the proof of strong subadditivity of the quantum entropy.
The very large transverse momenta and large multiplicities available in present LHC experiments on pp collisions allow a much closer look at the corresponding distributions. Some time ago we discussed a possible physical meaning of apparent…
With the discussion of three examples, we aim at clarifying the concept of energy transfer associated with dissipation in mechanics and in thermodynamics. The dissipation effects due to dissipative forces, such as the friction force between…
Entropy is a quantity which is of great importance in physics and chemistry. The concept comes out of thermodynamics, proposed by Rudolf Clausius in his analysis of Carnot cycle and linked by Ludwig Boltzmann to the number of specific ways…
Energy has an ambiguous status in general relativity. For systems embedded in asymptotically flat space-times it is possible to construct an integral invariant that corresponds to total energy, however there is no local differential…
Black hole thermodynamics suggests that the maximum entropy that can be contained in a region of space is proportional to the area enclosing it rather than its volume. I argue that this follows naturally from loop quantum gravity and a…
An important theme in recent work in asymptotic geometric analysis is that many classical implications between different types of geometric or functional inequalities can be reversed in the presence of convexity assumptions. In this note,…
We review and formulate results concerning log-concavity and strong-log-concavity in both discrete and continuous settings. We show how preservation of log-concavity and strongly log-concavity on $\mathbb{R}$ under convolution follows from…
Quantum theory's irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be…
These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…
The strong subadditivity of entropy plays a key role in several areas of physics and mathematics. It states that the entropy S[\rho]= - Tr (\rho \ln \rho) of a density matrix \rho_{123} on the product of three Hilbert spaces satisfies…
We show that the likelihood function for a multinomial vector observed under arbitrary interval censoring constraints on the frequencies or their partial sums is completely log-concave by proving that the constrained sample spaces comprise…
This paper describes an entropy equation, but one that should be used for measuring energy and not information. In relation to the human brain therefore, both of these quantities can be used to represent the stored information. The human…
The relationship between the intrinsic motion of gravity, light, and time is explored in terms of the principles of entropy, causality, energy, and symmetry conservation. A conceptual mechanism for gravity and the gravitational connection…
We show that the values of entropies of multidimensional shifts of finite type (SFTs) are characterized by a certain computation-theoretic property: a real number $h\geq 0$ is the entropy of such an SFT if and only if it is right…
The loop representation plays an important role in canonical quantum gravity because loop variables allow a natural treatment of the constraints. In these lectures we give an elementary introduction to (i) the relevant history of loops in…
It is well known that the KdV equation has an infinite set of conserved quantities. The first three are often considered to represent mass, momentum and energy. Here we try to answer the question of how this comes about, and also how these…