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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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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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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
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A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
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State Entropy and Differentiation Phenomenon.

Masanari Asano1, Irina Basieva2, Emmanuel M Pothos2

  • 1Liberal Arts Division, National Institute of Technology, Tokuyama College, Gakuendai, Shunan, Yamaguchi 745-8585, Japan.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

We introduce state entropy, a new measure generalizing von Neumann entropy to quantify state diversity in quantum systems. This helps analyze non-classical states during quantum measurement and models phenomena like cell differentiation.

Keywords:
density operatordifferentiationquantum measurementstate entropyvon Neumann entropy

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Area of Science:

  • Quantum Information Theory
  • Mathematical Physics
  • Complex Systems Analysis

Background:

  • Quantum states are described by density operators, which allow non-unique decompositions into pure state distributions.
  • Distributions can be classical (e.g., Schatten decomposition) or non-classical.
  • Understanding state diversity is crucial for analyzing quantum processes.

Purpose of the Study:

  • Define and introduce 'state entropy' as a novel measure.
  • Generalize the concept of von Neumann entropy to evaluate state distribution diversity.
  • Apply state entropy to analyze non-classical states during quantum measurement.

Main Methods:

  • Mathematical definition of state entropy.
  • Application of state entropy to analyze intermediate states in quantum measurement models.
  • Utilizing a differentiation model for step-by-step state transitions influenced by environmental factors.

Main Results:

  • State entropy quantifies the diversity of pure state distributions represented by a single density operator.
  • Demonstrated the utility of state entropy in analyzing non-classical states during quantum measurement.
  • The differentiation model provides a framework for observing state transitions.

Conclusions:

  • State entropy offers a new perspective on quantifying quantum state diversity.
  • The framework is applicable to understanding complex phenomena beyond quantum measurement, including biological and cognitive processes.
  • This work bridges quantum theory with the modeling of complex systems.