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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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Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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On Quantum Entropy.

Davi Geiger1, Zvi M Kedem1

  • 1Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA.

Entropy (Basel, Switzerland)
|July 8, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a new quantum entropy to measure randomness in quantum states, addressing limitations of existing measures. This quantum entropy may explain the arrow of time and particle creation in physics.

Keywords:
entropic uncertainty principlequantum entropyvon Neumann entropy

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Area of Science:

  • Quantum Information Theory
  • Quantum Thermodynamics
  • Particle Physics

Background:

  • Current quantum entropy measures, like von Neumann entropy, do not fully capture the randomness of quantum states.
  • Existing entropy definitions are insufficient for pure quantum states, where they trivially vanish.

Purpose of the Study:

  • To propose a novel quantum entropy measure that quantifies the randomness of pure quantum states.
  • To extend this new entropy definition to encompass mixed quantum states.
  • To investigate the implications of this quantum entropy for the arrow of time and particle physics.

Main Methods:

  • Defining a quantum entropy based on a conjugate pair of observables in quantum phase space.
  • Analyzing the properties of the proposed entropy, including its invariance under transformations and its relativistic scalar nature.
  • Examining the behavior of the quantum entropy during time evolution under a Dirac Hamiltonian and in scenarios involving entangled fermions.

Main Results:

  • The proposed quantum entropy quantifies the randomness of pure quantum states.
  • The entropy is dimensionless, a relativistic scalar, and invariant under canonical and CPT transformations.
  • Entropy monotonically increases during coherent state evolution but oscillates in entangled two-fermion systems.
  • A hypothesized entropy law suggests entropy never decreases in closed systems, implying a time arrow.

Conclusions:

  • The developed quantum entropy offers a more complete description of randomness in quantum systems.
  • Entropy oscillations in quantum systems might be linked to particle annihilation and creation.
  • The findings suggest a potential mechanism for the arrow of time in particle physics.