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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 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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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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The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
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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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Rényi's Entropy, Statistical Order and van der Waals Gas.

Flavia Pennini1,2, Angelo Plastino3

  • 1Departamento de Física, Universidad Católica del Norte, Av. Angamos 0610, Antofagasta 1270709, Chile.

Entropy (Basel, Switzerland)
|August 26, 2022
PubMed
Summary
This summary is machine-generated.

Statistical order arises from the disequilibrium concept, closely linked to Rényi entropy. This connection is further explored within the context of the van der Waals gas model.

Keywords:
Rényi’s entropycanonical ensembledisequilibriumvan der Waals

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Area of Science:

  • Statistical Mechanics
  • Thermodynamics
  • Information Theory

Background:

  • The concept of statistical order has roots in the disequilibrium principle.
  • This principle was introduced by López-Ruiz, Mancini, and Calbet.
  • Understanding statistical order is crucial in various scientific domains.

Purpose of the Study:

  • To demonstrate the intrinsic relationship between statistical disequilibrium and Rényi entropy.
  • To investigate the implications of this relationship in the context of the van der Waals gas model.
  • To provide a deeper understanding of statistical order and its physical manifestations.

Main Methods:

  • Theoretical analysis connecting disequilibrium and entropy measures.
  • Application of mathematical frameworks to explore statistical properties.
  • Utilizing the van der Waals gas model as a physical system for investigation.

Main Results:

  • A direct and intimate link between the disequilibrium measure and Rényi entropy is established.
  • The study confirms the relevance of this link in describing the behavior of the van der Waals gas.
  • Quantitative relationships are explored between these fundamental concepts.

Conclusions:

  • The disequilibrium concept provides a foundation for understanding statistical order.
  • Rényi entropy is a key measure intrinsically connected to statistical disequilibrium.
  • The van der Waals gas serves as a relevant model for observing these statistical phenomena.