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Entropy

Entropy

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...

The Second Law of Thermodynamics

The Second Law of Thermodynamics

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...

Entropy and the Second Law of Thermodynamics

Entropy and the Second Law of Thermodynamics

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...

Third Law of Thermodynamics

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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.

Entropy and Solvation

Entropy and Solvation

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...

Entropy Change in Reversible Processes

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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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Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

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Spin Entropy.

Davi Geiger¹, Zvi M Kedem¹

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

Entropy (Basel, Switzerland)

|September 23, 2022

Summary

This summary is machine-generated.

We introduce a new spin-entropy to quantify randomness in quantum states, addressing limitations of existing methods. This spin-entropy accurately measures quantum randomness and distinguishes between entangled and disentangled states.

Keywords:

entangled states geometric quantization spin entropy

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Area of Science:

Quantum mechanics
Information theory
Statistical mechanics

Background:

Quantum states possess two types of randomness: uncertainty in state coefficients and Born's rule probabilities.
Existing entropy measures, like von Neumann entropy, primarily quantify state specification randomness.
Previous entropies show limitations, e.g., higher values for entangled states despite greater constraint.

Purpose of the Study:

To propose a novel spin-entropy measure for quantum observables.
To accurately quantify randomness in both pure and mixed quantum states.
To overcome limitations of existing entropy measures, particularly for spin systems.

Main Methods:

Developed a spin-entropy based on the geometric quantization phase space of a spin.
Extended the spin-entropy formulation to mixed quantum states.
Analyzed spin-entropy for entangled and disentangled spin states.

Main Results:

The proposed spin-entropy quantifies both types of quantum randomness.
Spin-entropy never reaches zero, reflecting inherent quantum uncertainty.
Entangled states exhibit lower spin-entropy than disentangled states, aligning with observable constraints.

Conclusions:

The new spin-entropy provides a more comprehensive measure of quantum randomness.
This measure correctly differentiates randomness in entangled versus disentangled states.
Spin-entropy offers improved quantification of randomness in quantum information processing.