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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 and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

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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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Second Law of Thermodynamics

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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. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic...
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Statements of the Second Law of Thermodynamics01:15

Statements of the Second Law of Thermodynamics

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The second law of thermodynamics can be stated in several different ways, and all of them can be shown to imply the others. The Clausius’ statement of the second law of thermodynamics is based on the irreversibility of spontaneous heat flow. It states that heat will not flow from the colder body to the hotter body unless some other process is involved. Additionally, as per the Kelvin’s statement, it is impossible to convert the heat from a single source into work without any other...
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Maxwell's Thermodynamic Relations01:23

Maxwell's Thermodynamic Relations

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Maxwell's thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell's relations relates a partial differential between quantities that can be hard to measure experimentally to a partial differential between quantities that can be easily measured. These relations are a set of equations derivable from the symmetry of the second derivatives and the thermodynamic potentials.
All thermodynamic potentials are exact differentials. Therefore, their...
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Third Law of Thermodynamics02:38

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.
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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Quantum Thermodynamic Integrability for Canonical and Noncanonical Statistics.

R X Zhai1, C P Sun1

  • 1Graduate School of China Academy of Engineering Physics, Beijing 100193, China.

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|May 9, 2025
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Summary

We introduce quantum thermodynamic integrability (QTI) to extend the second law of thermodynamics. This new framework explains how temperature emerges and reveals informational correlations in finite quantum systems.

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Area of Science:

  • Quantum Thermodynamics
  • Statistical Mechanics
  • Quantum Information

Background:

  • The Carathéodory principle extends the second law of thermodynamics.
  • Quantum systems exhibit energy level dependence on macroscopic variables like volume and magnetic field.

Purpose of the Study:

  • To extend the Carathéodory principle to quantum thermodynamics.
  • To introduce quantum thermodynamic integrability (QTI) as a foundation for statistical mechanics.

Main Methods:

  • Extending the Carathéodory principle to quantum systems.
  • Defining QTI through path independence of work and heat.
  • Deriving canonical and noncanonical states from entropy integrable equations.

Main Results:

  • QTI is characterized by path independence in the thermodynamic manifold.
  • Temperature emerges as an integrating factor.
  • Noncanonical states reveal informational correlations in finite-size systems.

Conclusions:

  • QTI offers an alternative foundation for statistical mechanics.
  • The framework naturally derives canonical and noncanonical states.
  • Informational correlations are significant in finite quantum thermodynamic systems.