dorsal/arxiv
View SchemaGeneralised-Lorentzian Thermodynamics
| Authors | R. A. Treumann |
|---|---|
| Categories | |
| ArXiv ID | physics/9808037 |
| URL | https://arxiv.org/abs/physics/9808037 |
| DOI | 10.1238/Physica.Regular.059a00204 |
Abstract
We extend the recently developed non-gaussian thermodynamic formalism \cite{tre98} of a (presumably strongly turbulent) non-Markovian medium to its most general form that allows for the formulation of a consistent thermodynamic theory. All thermodynamic functions, including the definition of the temperature, are shown to be meaningful. The thermodynamic potential from which all relevant physical information in equilibrium can be extracted, is defined consistently. The most important findings are the following two: (1) The temperature is defined exactly in the same way as in classical statistical mechanics as the derivative of the energy with respect to the entropy at constant volume. (2) Observables are defined in the same way as in Boltzmannian statistics as the linear averages of the new equilibrium distribution function. This lets us conclude that the new state is a real thermodynamic equilibrium in systems capable of strong turbulence with the new distribution function replacing the Boltzmann distribution in such systems. We discuss the ideal gas, find the equation of state, and derive the specific heat and adiabatic exponent for such a gas. We also derive the new Gibbsian distribution of states. Finally we discuss the physical reasons for the development of such states and the observable properties of the new distribution function.
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"abstract": "We extend the recently developed non-gaussian thermodynamic formalism\n\\cite{tre98} of a (presumably strongly turbulent) non-Markovian medium to its\nmost general form that allows for the formulation of a consistent thermodynamic\ntheory. All thermodynamic functions, including the definition of the\ntemperature, are shown to be meaningful. The thermodynamic potential from which\nall relevant physical information in equilibrium can be extracted, is defined\nconsistently. The most important findings are the following two: (1) The\ntemperature is defined exactly in the same way as in classical statistical\nmechanics as the derivative of the energy with respect to the entropy at\nconstant volume. (2) Observables are defined in the same way as in Boltzmannian\nstatistics as the linear averages of the new equilibrium distribution function.\nThis lets us conclude that the new state is a real thermodynamic equilibrium in\nsystems capable of strong turbulence with the new distribution function\nreplacing the Boltzmann distribution in such systems. We discuss the ideal gas,\nfind the equation of state, and derive the specific heat and adiabatic exponent\nfor such a gas. We also derive the new Gibbsian distribution of states. Finally\nwe discuss the physical reasons for the development of such states and the\nobservable properties of the new distribution function.",
"arxiv_id": "physics/9808037",
"authors": [
"R. A. Treumann"
],
"categories": [
"physics.space-ph",
"physics.plasm-ph"
],
"doi": "10.1238/Physica.Regular.059a00204",
"title": "Generalised-Lorentzian Thermodynamics",
"url": "https://arxiv.org/abs/physics/9808037"
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