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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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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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Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.
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True weight is the measure of the gravitational force acting on an object. However, if the object accelerates, its measured weight is different from its true weight. Similar observations can be made when the object is submerged in water. An object's weight in water is its apparent weight, which is equal to the difference between its true weight and the buoyant forces.
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Aggregate shape is classified based on the relative sharpness or roundness of the edges and corners. This classification includes categories like rounded, angular, elongated, and flaky, each with specific characteristics. Rounded aggregates, fully shaped by attrition, are typical of river or seashore gravel, while angular aggregates, such as crushed rock, have well-defined edges. Aggregates that are elongated and flaky are less desirable, as they can reduce the workability and strength of...
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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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Decoding the Apparent Horizon: Coarse-Grained Holographic Entropy.

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Black hole formation in holographic theories preserves interior information on the boundary. The apparent horizon

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Area of Science:

  • Theoretical physics
  • Quantum gravity
  • Black hole thermodynamics

Background:

  • Information paradox in black holes
  • Holographic principle and AdS/CFT correspondence
  • Entanglement entropy in quantum field theory

Purpose of the Study:

  • To prove the relationship between black hole apparent horizon area and interior information entropy.
  • To establish the maximum holographic entanglement entropy compatible with external measurements.
  • To identify the boundary dual to this entropy and verify thermodynamic laws.

Main Methods:

  • Mathematical derivation within holographic theories.
  • Analysis of information encoding in black hole interiors.
  • Application of coarse-graining techniques to interior information.

Main Results:

  • The area of the apparent horizon precisely quantifies the coarse-grained interior information entropy.
  • This entropy represents the maximum holographic entanglement entropy consistent with exterior geometry.
  • Identification of the specific boundary dual to this holographic entanglement entropy.

Conclusions:

  • Black hole horizon area is a direct measure of hidden interior information.
  • The holographic principle provides a framework for understanding information preservation.
  • The identified boundary dual confirms the second law of thermodynamics for black holes.