scholarly journals Quantum and Classical Ergotropy from Relative Entropies

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1107
Author(s):  
Akira Sone ◽  
Sebastian Deffner
Keyword(s):  
Quantum Mechanics ◽  
Quantum State ◽  
Relative Entropy ◽  
Thermal State ◽  
Unified Approach ◽  
Maximum Work ◽  
The Difference ◽  
Energy Surfaces ◽  
Geometric Quantum Mechanics ◽  
Thermal States

The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of the quantum state with respect to the thermal state, we define the classical ergotropy, which quantifies how much work can be extracted from distributions that are inhomogeneous on the energy surfaces. A unified approach to treat both quantum as well as classical scenarios is provided by geometric quantum mechanics, for which we define the geometric relative entropy. The analysis is concluded with an application of the conceptual insight to conditional thermal states, and the correspondingly tightened maximum work theorem.

A novel q-rung orthopair fuzzy TODIM approach for multi-criteria group decision making based on Shapley value and relative entropy

2021 ◽  
Vol 40 (1) ◽  
pp. 235-250
Author(s):  
Liuxin Chen ◽  
Nanfang Luo ◽  
Xiaoling Gou
Keyword(s):  
Decision Making ◽  
Relative Entropy ◽  
Group Decision Making ◽  
Shapley Value ◽  
Group Decision ◽  
Similarity Measures ◽  
Entropy Measure ◽  
Shapley Values ◽  
Interactive Relationship ◽  
The Difference

In the real multi-criteria group decision making (MCGDM) problems, there will be an interactive relationship among different decision makers (DMs). To identify the overall influence, we define the Shapley value as the DM’s weight. Entropy is a measure which makes it better than similarity measures to recognize a group decision making problem. Since we propose a relative entropy to measure the difference between two systems, which improves the accuracy of the distance measure.In this paper, a MCGDM approach named as TODIM is presented under q-rung orthopair fuzzy information.The proposed TODIM approach is developed for correlative MCGDM problems, in which the weights of the DMs are calculated in terms of Shapley values and the dominance matrices are evaluated based on relative entropy measure with q-rung orthopair fuzzy information.Furthermore, the efficacy of the proposed Gq-ROFWA operator and the novel TODIM is demonstrated through a selection problem of modern enterprises risk investment. A comparative analysis with existing methods is presented to validate the efficiency of the approach.

scholarly journals Supreme Theory of Everything

2019 ◽  
Vol 2 (2) ◽  
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Electromagnetic Wave ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Wave Particle Duality ◽  
Theory Of Everything ◽  
Parallel Universes ◽  
Celestial Bodies ◽  
Geometric Quantum Mechanics

Not only universe, but everything has general characters as eternal, infinite, cyclic and wave-particle duality. Everything from elementary particles to celestial bodies, from electromagnetic wave to gravity is in eternal motions, which dissects only to circle. Since everything is described only by trigonometry. Without trigonometry and mathematical circle, the science cannot indicate all the beauty of harmonic universe. Other method may be very good, but it is not perfect. Some part is very nice, another part is problematic. General Theory of Relativity holds that gravity is geometric. Quantum Mechanics describes all particles by wave function of trigonometry. In this paper using trigonometry, particularly mathematics circle, a possible version of the unification of partial theories, evolution history and structure of expanding universe, and the parallel universes are shown.

Remarks on geometric quantum mechanics

2004 ◽  
Vol 51 (2) ◽  
pp. 229-243 ◽  
Author(s):  
Alberto Benvegnù ◽  
Nicola Sansonetto ◽  
Mauro Spera
Keyword(s):  
Quantum Mechanics ◽  
Geometric Quantum Mechanics

Indeterminacy

2020 ◽  
pp. 172-184
Author(s):  
Alastair Wilson
Keyword(s):  
Quantum Mechanics ◽  
Quantum State ◽  
Modal Realism ◽  
Many Worlds ◽  
Philosophical Literature ◽  
Universal Quantum ◽  
Quantum Indeterminacy

In Everettian quantum mechanics, the universal quantum state is fundamental, non-contingent, and wholly determinate. By contrast, the parallel worlds of diverging EQM, and the contingency constituted by self-location amongst those worlds, are emergent and partly indeterminate. In particular, it is indeterminate both how many worlds there are, and what microscopic qualitative features those worlds have. This chapter discusses various ways to understand indeterminacy in the Everettian multiverse, and argues that the indeterminacies of EQM present no obstacle to the analytic ambitions of quantum modal realism. Everettians can understand quantum indeterminacy using models of indeterminacy that are familiar from the philosophical literature on vagueness.

No-cloning Theorem and Quantum Copying

2020 ◽  
pp. 172-181
Author(s):  
M. Suhail Zubairy
Keyword(s):  
Quantum Mechanics ◽  
Quantum State ◽  
Uncertainty Relation ◽  
Foundations Of Quantum Mechanics ◽  
Quantum Cloning ◽  
Foundation Of Quantum Mechanics ◽  
Quantum Copying ◽  
Arbitrary Quantum ◽  
Principle Of Complementarity

Heisenberg’s uncertainty relation and Bohr’s principle of complementarity form the foundations of quantum mechanics. If these are violated then the edifice of quantum mechanics can come crashing down. In this chapter, it is shown how cloning or perfect copying of a quantum state can potentially lead to a violation of these sacred principles. A no-cloning theorem is proven showing that the cloning of an arbitrary quantum state is not allowed. The foundation of quantum mechanics is therefore protected. It is also shown how quantum cloning can lead to superluminal communication. It is also discussed that, if making a perfect copy of a quantum state is forbidden, how best a copy of a state can be made.

scholarly journals Twenty Years of Quantum State Teleportation at the Sapienza University in Rome

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 768 ◽  
Author(s):  
Francesco De De Martini ◽  
Fabio Sciarrino
Keyword(s):  
Quantum Mechanics ◽  
Quantum Optics ◽  
Quantum State ◽  
Quantum Teleportation ◽  
Feed Forward ◽  
Unknown Quantum State ◽  
University Of Rome ◽  
The University ◽  
First Time

Quantum teleportation is one of the most striking consequence of quantum mechanics and is defined as the transmission and reconstruction of an unknown quantum state over arbitrary distances. This concept was introduced for the first time in 1993 by Charles Bennett and coworkers, it has then been experimentally demonstrated by several groups under different conditions of distance, amount of particles and even with feed forward. After 20 years from its first realization, this contribution reviews the experimental implementations realized at the Quantum Optics Group of the University of Rome La Sapienza.

CO2 balance of a heterothermic rodent: comparison of sleep, torpor, and awake states

1984 ◽  
Vol 246 (1) ◽  
pp. R49-R55 ◽  
Author(s):  
P. E. Bickler
Keyword(s):  
Ground Squirrel ◽  
Lung Ventilation ◽  
Body Fluids ◽  
The Body ◽  
Metabolic Intensity ◽  
Co2 Balance ◽  
The Difference ◽  
Tb 32 ◽  
Total Body ◽  
Thermal States

CO2 homeostasis of different thermal states have been compared in a heterothermic ground squirrel, Spermophilus tereticaudus. Gas exchange (MO2, MCO2), lung ventilation (VE), and body temperature (Tb) were simultaneously measured during sleep, shallow torpor (Tb 25-29 degrees C), deep torpor (Tb 11-15 degrees C), awake heterothermia (Tb 30-42.5 degrees C), and transitions between these states. CO2 retention (falling MCO2/MO2 and VE/MCO2) accompanied entrance into sleep and torpor. CO2 retention lowered MO2 in sleeping and torpid squirrels beyond that caused by reduced Tb. In torpor at steady state, MCO2/MO2 (R) and ventilation returned to control values, and no further CO2 retention occurred. Arousal from sleep or torpor was accompanied by transiently high VE/MCO2 and R values as CO2 was released from the body fluids. R and VE/MCO2 values during heterothermia in awake squirrels (Tb 32-42.5 degrees C) showed that total body CO2 content remained unchanged until Tb reached 40 degrees C with onset of hyperventilation. Altered CO2 content of the body fluids is thus not a general feature of mammalian heterothermy. The difference in CO2 homeostasis of torpid and heterothermic awake animals may have implications for the difference in metabolic intensity of these states.

scholarly journals Mechanism and kinetics for both thermal and electrochemical reduction of N2 catalysed by Ru(0001) based on quantum mechanics

2019 ◽  
Vol 21 (32) ◽  
pp. 17605-17612 ◽  
Author(s):  
Liang-Yu Chen ◽  
Tung-Chun Kuo ◽  
Zih-Siang Hong ◽  
Mu-Jeng Cheng ◽  
William A. Goddard
Keyword(s):  
Free Energy ◽  
Quantum Mechanics ◽  
Electrochemical Reduction ◽  
Mechanism And Kinetics ◽  
Energy Surfaces

QM calculations were used to predict the free energy surfaces for N2 thermal and electrochemical reduction (N2TR and N2ER) on Ru(0001), to find the detailed atomistic mechanism and kinetics, and provide the basis for improving the efficiency of N2ER.

scholarly journals Comparing Information Metrics for a Coupled Ornstein–Uhlenbeck Process

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 775 ◽  
Author(s):  
James Heseltine ◽  
Eun-jin Kim
Keyword(s):  
Relative Entropy ◽  
Uhlenbeck Process ◽  
Relaxation Problem ◽  
Ornstein Uhlenbeck Process ◽  
Long Time ◽  
The Difference ◽  
Information Change ◽  
Information Metrics ◽  
Insight Into ◽  
Linear Geometry

It is often the case when studying complex dynamical systems that a statistical formulation can provide the greatest insight into the underlying dynamics. When discussing the behavior of such a system which is evolving in time, it is useful to have the notion of a metric between two given states. A popular measure of information change in a system under perturbation has been the relative entropy of the states, as this notion allows us to quantify the difference between states of a system at different times. In this paper, we investigate the relaxation problem given by a single and coupled Ornstein–Uhlenbeck (O-U) process and compare the information length with entropy-based metrics (relative entropy, Jensen divergence) as well as others. By measuring the total information length in the long time limit, we show that it is only the information length that preserves the linear geometry of the O-U process. In the coupled O-U process, the information length is shown to be capable of detecting changes in both components of the system even when other metrics would detect almost nothing in one of the components. We show in detail that the information length is sensitive to the evolution of subsystems.

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