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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.
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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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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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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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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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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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Relativistic Roots of κ-Entropy.

Giorgio Kaniadakis1

  • 1Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.

Entropy (Basel, Switzerland)
|May 24, 2024
PubMed
Summary
This summary is machine-generated.

The κ-statistical theory is proven with five axioms, unifying simple and complex systems. This framework, based on κ-entropy, extends beyond physics and addresses long-standing relativistic physics problems.

Keywords:
power-law tailed distributionsrelativistic statistical mechanicsrelativistic temperaturerelativistic thermodynamicstemperature of a moving bodyκ-deformationκ-entropyκ-exponentialκ-logarithmκ-mathematicsκ-statisticsκdistribution

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Area of Science:

  • Statistical Mechanics
  • Information Theory
  • Relativistic Physics

Background:

  • The standard Khinchin-Shannon axioms form the basis of classical statistical mechanics.
  • Existing theories face challenges in unifying simple and complex systems and addressing relativistic effects.

Purpose of the Study:

  • To rigorously prove the axiomatic structure of the κ-statistical theory.
  • To demonstrate that κ-entropy and Boltzmann-Gibbs-Shannon entropy derive from a unified set of five axioms.
  • To explore the applicability of κ-entropy beyond physics and its connection to relativistic principles.

Main Methods:

  • Axiomatic formulation of κ-statistical theory.
  • Derivation of κ-entropy and Boltzmann-Gibbs-Shannon entropy from five axioms.
  • Investigation of the physical origins of self-duality and scaling axioms in relativistic physics.

Main Results:

  • The κ-statistical theory is established upon five axioms, including self-duality and scaling.
  • Both κ-entropy and Boltzmann-Gibbs-Shannon entropy are shown to be consequences of these axioms.
  • The κ-formalism unifies the treatment of simple and complex systems.
  • Relativistic statistical mechanics based on κ-entropy retains key features of classical statistical mechanics.
  • The theory provides solutions to open problems in relativistic physics concerning the speed-dependence of thermodynamic quantities.

Conclusions:

  • The κ-statistical theory offers a unified framework for statistical mechanics, applicable to diverse complex systems.
  • The theory's foundation in relativistic principles resolves long-standing issues in physics.
  • κ-entropy provides a generalized approach to information and statistical mechanics.