21 papers · ranked by Valyu relevance
Edward Witten
This article consists of a very short introduction to classical and quantum information theory. Basic properties of the classical Shannon entropy and the quantum von Neumann entropy are described, along with related concepts such as classical and quantum relative entropy, conditional entropy, and mutual information. A…
Lluís A. Belanche-Muñoz, Małgorzata Wiejacha, Jose C. Principe
Kernel methods have played a major role in the last two decades in the modeling and visualization of complex problems in data science. The choice of kernel function remains an open research area and the reasons why some kernels perform better than others are not yet understood. Moreover, the high computational costs of…
Cal R. Abel
This work presents a generalization of game theory and new perspectives on utility and value. Using quantum formalism, we prove that classical game theory is a special case of quantum game theory. We show that the von Neumann entropy and von Neumann-Morgenstern utility are equivalent and that the Hamiltonian operator…
Salomé A. Sepúlveda-Fontaine, José M. Amigó, Sotiris Kotsiantis
Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory, Ergodic Theory and the Theory of Dynamical Systems. Specifically, we are referring…
Paolo Facchi, Giovanni Gramegna, Arturo Konderak, Rosario Lo Franco
Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a minimality property of the von Neumann entropy of a density matrix with respect to…
Claudia L. Clarke, Ian J. Ford, Welles Antonio Martinez Morgado, Silvio Manuel Duarte Queiros
'Silvio Manuel Duarte Queiros'] The reduced density matrix that characterises the state of an open quantum system is a projection from the full density matrix of the quantum system and its environment, and there are many full density matrices consistent with a given reduced version. Without a specification of relevant…
Alexey V. Melkikh, Ronnie Kosloff, Rosario Lo Franco
Quantum entanglement can cause the efficiency of a heat engine to be greater than the efficiency of the Carnot cycle. However, this does not mean a violation of the second law of thermodynamics, since there is no local equilibrium for pure quantum states, and, in the absence of local equilibrium, thermodynamics cannot…
Eugene Y. S. Chua
Conventional wisdom holds that the von Neumann entropy corresponds to thermodynamic entropy, but Hemmo and Shenker (2006) have recently argued against this view by attacking von Neumann's (1955) argument. I argue that Hemmo and Shenker's arguments fail due to several misunderstandings: about statistical-mechanical and…
Kavana Priyadarshini Keshava, Dieter W. Heermann, Arnab Bhattacherjee
Hi-C and related 3C technologies capture 3D genome architecture by measuring contact frequencies between genomic loci. These contact maps are often sparse and noisy, making comparison across samples challenging. Traditional metrics such as Pearson’s correlation fail to capture their structural complexity. To address…
Paolo Facchi, Giovanni Gramegna, Arturo Konderak
Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a minimality property of the von Neumann entropy of a density matrix with respect to…
Haiqi Wu, Kai Xu
This paper investigates the relationship between categorical entropy and von Neumann entropy of quantum lattices. We begin by studying the von Neumann entropy, proving that the average von Neumann entropy per site converges to the logarithm of an algebraic integer in the low-temperature and thermodynamic limits. Next…
Carina Prunkl
In 1932, von Neumann argued for the equivalence of the thermodynamic entropy and −Trρ ln ρ, since known as the von Neumann entropy. Hemmo and Shenker (2006) recently challenged this argument by pointing out an alleged discrepancy between the two entropies in the single particle case, concluding that they must be…
Marek Sawerwain, Joanna Wiśniewska, Roman Gielerak, Jaroslaw Miszczak + 1 more
'Jaroslaw Miszczak' 'Zbigniew Puchała'] Information switching and swapping seem to be fundamental elements of quantum communication protocols. Another crucial issue is the presence of entanglement and its level in inspected quantum systems. In this article, a formal definition of the operation of the swapping local…
Carlo Nicolini, Giulia Forcellini, Ludovico Minati, Angelo Bifone
Functional connectivity is derived from inter-regional correlations in spontaneous fluctuations of brain activity, and can be represented in terms of complete graphs with continuous (real-valued) edges. The structure of functional connectivity networks is strongly affected by signal processing procedures to remove the…
Erin Sheridan
Recently, attention has returned to the now-famous 1932 thought experiment in which John von Neumann establishes the form of the quantum mechanical von Neumann entropy −Trln (), supposedly by arguing for its correspondence with the phenomenological thermodynamic entropy (.) Hemmo and Shenker (2006) reconstruct von…
Elizabeth A Stoll
Neuronal populations in the cerebral cortex engage in probabilistic coding, effectively encoding the state of the surrounding environment with high accuracy and extraordinary energy efficiency. A new approach models the inherently probabilistic nature of cortical neuron signaling outcomes as a thermodynamic process of…
Elizabeth A Stoll
In cortical neurons, spontaneous membrane potential fluctuations affect the likelihood of firing an action potential. Yet despite retaining sensitivity to random electrical noise in gating signaling outcomes, these cells achieve highly accurate computations with extraordinary energy efficiency. A new approach models…
Authors not listed
Gibbs’ paradox—the apparent discontinuity in mixing entropy for gases of varying similarity and the seeming reversibility of mixing-separation cycles—has resisted fully satisfactory resolution for 150 years. We present a solution based on categorical state theory, which posits that physical con f igurations are…
Mohsen Farshad
Providing a simple description of entropy as the foundation of thermodynamics is necessary for researchers in explaining physical phenomena in the universe. Here we dive deep into the meaning of entropy starting from the basics and ending with the Newton's second law of motion which may be rooted in a hidden dimension…
Umberto Lucia, Giulia Grisolia
Causality is the relationship between causes and effects. Following Relativity, any cause of an event must always be in the past light cone of the event itself, but causes and effect must always be related to some interactions. In this paper, causality is developed as a consequence of the analysis of the Einstein…
Ahmed Elewa
A time dilation factor is derived from information entropy via the holographic principle. By imagining the embryonic cell as a hologram, time dilation during embryogenesis is predicted from the entropy of active genetic information and shown to be consistent with observed lengths of cell duration. The connection…