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Entropy02:39

Entropy

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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.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
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Entropy and the Second Law of Thermodynamics01:20

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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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Third Law of Thermodynamics02:38

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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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Entropy and Solvation02:05

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The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ...
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Entropy Change in Reversible Processes01:10

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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.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
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The von Neumann Entropy for Mixed States.

Jorge A Anaya-Contreras1, Héctor M Moya-Cessa2, Arturo Zúñiga-Segundo1

  • 1Instituto Politécnico Nacional, ESFM Departamento de Física, Edificio 9 Unidad Profesional Adolfo López Mateos, 07738 México D.F., Mexico.

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

This study extends the Araki-Lieb inequality to calculate quantum entropy for mixed states. Researchers successfully determined the von Neumann entropy for large quantum systems, specifically in two-level atom-field interactions.

Keywords:
Araki–Lieb inequalityatom-field interactionmixed statesvon Neumann entropy

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Area of Science:

  • Quantum Information Theory
  • Statistical Mechanics
  • Atomic Physics

Background:

  • The Araki-Lieb inequality is crucial for calculating subsystem entropy in pure initial states.
  • Calculating entropy for subsystems initially in mixed states remains a challenge.
  • Existing methods struggle when dealing with mixed initial states in quantum systems.

Purpose of the Study:

  • To develop a method for calculating quantum entropy when one subsystem is initially in a mixed state.
  • To extend the applicability of the Araki-Lieb inequality.
  • To determine the von Neumann entropy for large quantum systems in specific interaction scenarios.

Main Methods:

  • Application of the Araki-Lieb inequality to a system with a mixed initial state.
  • Analysis of a two-level atom interacting with a quantized field.
  • Derivation of the von Neumann entropy for the larger subsystem.

Main Results:

  • Demonstrated a novel method to calculate quantum entropy for mixed initial states.
  • Successfully applied the Araki-Lieb inequality in a scenario previously considered intractable.
  • Obtained the von Neumann entropy for an infinite system in the context of atom-field interaction.

Conclusions:

  • The Araki-Lieb inequality can be effectively used to calculate von Neumann entropy even when subsystems start in mixed states.
  • This work provides a new pathway for entropy calculations in complex quantum systems.
  • The findings have implications for understanding quantum information in diverse physical settings.