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Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation  between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
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Entropy02:39

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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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Entropy01:18

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The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
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In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
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The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
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The coefficient of variation measures the dispersion of the data points or distribution around the mean. Using the coefficient of variation, we can compare two data series with drastically different means or different units of measurement. The coefficient of variation for a sample and a population is expressed as a percentage of the ratio of standard deviation to the mean.
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Maximum Relative Entropy of Coherence: An Operational Coherence Measure.

Kaifeng Bu1, Uttam Singh2,3, Shao-Ming Fei4,5

  • 1School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, People's Republic of China.

Physical Review Letters
|October 28, 2017
PubMed
Summary
This summary is machine-generated.

We introduce a new quantum coherence quantifier based on maximum relative entropy. This quantifier offers operational interpretations and quantifies advantages in subchannel discrimination tasks.

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Area of Science:

  • Quantum Information Theory
  • Quantum Thermodynamics

Background:

  • Quantum coherence is a fundamental resource in quantum information science.
  • The resource theory of coherence requires robust methods for quantifying coherence.
  • Existing quantifiers may lack direct operational interpretations.

Purpose of the Study:

  • To introduce and characterize a novel quantifier for quantum coherence based on maximum relative entropy.
  • To establish an operational interpretation for this new coherence measure.
  • To explore its utility in understanding the advantages of coherent states in specific quantum information processing tasks.

Main Methods:

  • Development of a new coherence quantifier using maximum relative entropy.
  • Mathematical proofs establishing connections between the quantifier and operational tasks.
  • Analysis of smooth versions of the quantifier for one-shot scenarios.
  • Investigation of the asymptotic behavior of the quantifier.

Main Results:

  • The maximum relative entropy of coherence is operationally interpreted via maximum overlap with maximally coherent states.
  • Coherent states exhibit advantages in subchannel discrimination, precisely characterized by this quantifier.
  • Smooth maximum relative entropy of coherence provides a lower bound for one-shot coherence cost.
  • Minimum relative entropy of coherence offers an upper bound for one-shot coherence distillation.

Conclusions:

  • The proposed maximum relative entropy of coherence provides a valuable tool for quantifying quantum coherence.
  • This quantifier offers clear operational meaning and bounds for quantum resource manipulation.
  • The findings contribute to the theoretical framework of quantum resource theories.