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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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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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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
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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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On Higher Order Structures in Thermodynamics.

Valentin Lychagin1, Mikhail Roop1,2

  • 1V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya Str., 117997 Moscow, Russia.

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Summary
This summary is machine-generated.

This study develops measurement-based thermodynamics, describing states as geometric manifolds. It introduces higher-order structures derived from measurement variances, enhancing the understanding of thermodynamic processes and states.

Keywords:
Legendrian and Lagrangian manifoldsskewnessthermodynamic statesvariance

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Area of Science:

  • Thermodynamics
  • Mathematical Physics
  • Statistical Mechanics

Background:

  • Classical thermodynamics traditionally focuses on macroscopic variables.
  • Thermodynamic states can be represented by geometric structures like manifolds.
  • Measurement is fundamental to physical theories.

Purpose of the Study:

  • To develop a measurement-based approach to classical thermodynamics.
  • To explore the geometric representation of thermodynamic states.
  • To investigate higher-order structures in thermodynamics derived from measurement.

Main Methods:

  • Representing thermodynamic states as Legendre or Lagrangian manifolds.
  • Utilizing the variance of random vectors to induce Riemannian structures.
  • Computing higher-order central moments (cubic and fourth-order forms).

Main Results:

  • Thermodynamic states are described as manifolds representing averages and extremal measures.
  • Measurement variances induce Riemannian structures on these manifolds.
  • Higher-order structures (cubic and fourth-order forms) reveal skewness and additional state requirements.

Conclusions:

  • A measurement-based framework provides a novel perspective on thermodynamics.
  • Geometric structures and higher-order moments offer deeper insights into thermodynamic states and processes.
  • The study links statistical properties (moments) to fundamental thermodynamic requirements.