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Related Concept Videos

Entropy01:18

Entropy

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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 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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Acid-Catalyzed Hydration of Alkenes02:45

Acid-Catalyzed Hydration of Alkenes

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Alkenes react with water in the presence of an acid to form an alcohol. In the absence of acid, hydration of alkenes does not occur at a significant rate, and the acid is not consumed in the reaction. Therefore, alkene hydration is an acid-catalyzed reaction.
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Catalysis02:50

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The presence of a catalyst affects the rate of a chemical reaction. A catalyst is a substance that can increase the reaction rate without being consumed during the process. A basic comprehension of a catalysts’ role during chemical reactions can be understood from the concept of reaction mechanisms and energy diagrams.
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A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
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The Second Law of Thermodynamics01:14

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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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Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes
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Entropy and Reversible Catalysis.

H Wilming1

  • 1Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland and Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany.

Physical Review Letters
|January 14, 2022
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Summary
This summary is machine-generated.

Nondecreasing entropy is key for reversible state transformations in quantum and classical systems. This finding resolves the catalytic entropy conjecture and offers a single-shot characterization of entropy.

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Area of Science:

  • Quantum Information Theory
  • Statistical Mechanics
  • Information Theory

Background:

  • Catalytic processes are crucial for state transformations in physical systems.
  • The catalytic entropy conjecture proposed a condition for such transformations.
  • Understanding entropy's role in reversible processes is fundamental.

Purpose of the Study:

  • To establish a necessary and sufficient condition for state conversion using catalysts.
  • To resolve the approximate catalytic entropy conjecture.
  • To provide a single-shot characterization of von Neumann and Shannon entropies.

Main Methods:

  • Proving theorems for finite-dimensional quantum mechanics using von Neumann entropy.
  • Proving theorems for classical systems with probability distributions using Shannon entropy.
  • Comparing results with phenomenological thermodynamics.

Main Results:

  • Nondecreasing entropy is proven to be a necessary and sufficient condition for reversible catalytic state transformations.
  • The catalytic entropy conjecture is affirmatively resolved.
  • A complete single-shot characterization of von Neumann and Shannon entropies is achieved without external randomness.

Conclusions:

  • The study provides a fundamental understanding of entropy in reversible transformations.
  • The findings have implications for quantum statistical mechanics, including characterizing Gibbs states.
  • This work unifies concepts across quantum and classical information theory.