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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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Second Law of Thermodynamics02:49

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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 models, the...
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Second Law of Thermodynamics00:53

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The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the...
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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 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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Entropy Production in Exactly Solvable Systems.

Luca Cocconi1,2,3, Rosalba Garcia-Millan1,2,4, Zigan Zhen1,2

  • 1Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

This study reviews entropy production, a measure of deviation from thermodynamic equilibrium. It calculates entropy production in exactly solvable systems, offering a foundation for complex non-equilibrium systems.

Keywords:
active matterentropy productionexact resultsstochastic thermodynamics

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Stochastic Processes

Background:

  • Entropy production quantifies a system's distance from thermodynamic equilibrium.
  • It measures the breaking of global detailed balance and time-reversal symmetry.
  • A lack of comprehensive examples hinders understanding of entropy production fundamentals.

Purpose of the Study:

  • To provide a self-contained review of entropy production.
  • To calculate entropy production from first principles in exactly solvable systems.
  • To offer a benchmark for studying complex non-equilibrium systems.

Main Methods:

  • Review of entropy production fundamentals.
  • First-principles calculation of entropy production.
  • Analysis of discrete- and continuous-state Markov processes.
  • Examination of single- and multiple-particle systems.

Main Results:

  • A catalogue of exactly solvable setups for entropy production calculation.
  • Demonstration of entropy production in diverse Markov processes.
  • Foundation for analyzing more complex systems like active matter.

Conclusions:

  • The presented examples serve as a stepping stone for advanced studies.
  • This work provides a benchmark for developing new mathematical formalisms.
  • Understanding entropy production is crucial for non-equilibrium statistical mechanics.