Articles | Volume 25, issue 1
https://doi.org/10.5194/npg-25-77-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Special issue:
https://doi.org/10.5194/npg-25-77-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Derivation of the entropic formula for the statistical mechanics of space plasmas
George Livadiotis
CORRESPONDING AUTHOR
Southwest Research Institute, Space Science and Engineering, San
Antonio, TX, USA
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Cited
35 citations as recorded by crossref.
- Forced KdV and Envelope Soliton in Magnetoplasma With Kappa Distributed Ions J. Sarkar et al.
- Rankine–Hugoniot Shock Conditions for Space and Astrophysical Plasmas Described by Kappa Distributions G. Livadiotis
- Physical Correlations Lead to Kappa Distributions G. Livadiotis & D. McComas
- Collision frequency and mean free path for plasmas described by kappa distributions G. Livadiotis
- Nonextensive Statistical Mechanics: Equivalence Between Dual Entropy and Dual Probabilities G. Livadiotis
- Study of ideal gases in curved spacetimes L. Aragón-Muñoz & H. Quevedo
- Fokker-Planck equation for Coulomb relaxation and wave-particle diffusion: Spectral solution and the stability of the Kappa distribution to Coulomb collisions W. Zhang & B. Shizgal
- Thermodynamics of the Inner Heliosheath G. Livadiotis et al.
- Impact of Quantum Non-Locality and Electronic Non-Ideality on the Shannon Entropy for Atomic States in Dense Plasma A. Nuraly et al.
- Complex Systems Methods Characterizing Nonlinear Processes in the Near-Earth Electromagnetic Environment: Recent Advances and Open Challenges G. Balasis et al.
- Kappa-tail Technique: Modeling and Application to Solar Energetic Particles Observed by Parker Solar Probe G. Livadiotis et al.
- Evaluating the Adiabatic Invariants in Magnetized Plasmas Using a Classical Ehrenfest Theorem A. Tamburrini et al.
- Multimode excitation and modulational instability of beam plasma system with Tsallis-distributed electrons P. Bala & T. Gill
- Thermodynamics of Pickup Ions in the Heliosphere G. Livadiotis et al.
- On the origin of the polytropic behavior in space plasmas G. Livadiotis
- Kappa and other nonequilibrium distributions from the Fokker-Planck equation and the relationship to Tsallis entropy B. Shizgal
- Thermodynamic Definitions of Temperature and Kappa and Introduction of the Entropy Defect G. Livadiotis & D. McComas
- Slowing down of charged particles in dusty plasmas with power‐law kappa‐distributions J. Du et al.
- Polytropes in plasmas described by kappa distributions – Application in atmospheric modelling G. Livadiotis
- Long-Term Independence of Solar Wind Polytropic Index on Plasma Flow Speed G. Livadiotis
- Thermodynamic Constraints on Solar Wind Radial Profiles G. Livadiotis & D. McComas
- Blackbody radiation, kappa distribution and superstatistics E. Gravanis & E. Akylas
- Energetic particle distributions in space physics represented by the Pearson differential equation for the kappa distribution B. Shizgal
- The theory of thermodynamic relativity G. Livadiotis & D. McComas
- Universality of kappa distributions G. Livadiotis & D. McComas
- What Defines Stationarity in Space Plasmas G. Livadiotis & D. McComas
- Thermodynamic origin of kappa distributions G. Livadiotis
- Superstatistics from a dynamical perspective: Entropy and relaxation K. Ourabah
- Preface: Nonlinear waves and chaos G. Lakhina et al.
- Kappa Distributions: Statistical Physics and Thermodynamics of Space and Astrophysical Plasmas G. Livadiotis
- Stability of three-dimensional dust acoustic waves in a strongly coupled dusty plasma including kappa distributed superthermal ions and electrons W. El-Taibany et al.
- Anisotropic Kappa Distributions. I. Formulation Based on Particle Correlations G. Livadiotis et al.
- Entropy defect in thermodynamics G. Livadiotis & D. McComas
- Thermal Doppler Broadening of Spectral Emissions in Space and Astrophysical Plasmas G. Livadiotis
- Theoretical aspects of Hamiltonian kappa distributions G. Livadiotis
35 citations as recorded by crossref.
- Forced KdV and Envelope Soliton in Magnetoplasma With Kappa Distributed Ions J. Sarkar et al.
- Rankine–Hugoniot Shock Conditions for Space and Astrophysical Plasmas Described by Kappa Distributions G. Livadiotis
- Physical Correlations Lead to Kappa Distributions G. Livadiotis & D. McComas
- Collision frequency and mean free path for plasmas described by kappa distributions G. Livadiotis
- Nonextensive Statistical Mechanics: Equivalence Between Dual Entropy and Dual Probabilities G. Livadiotis
- Study of ideal gases in curved spacetimes L. Aragón-Muñoz & H. Quevedo
- Fokker-Planck equation for Coulomb relaxation and wave-particle diffusion: Spectral solution and the stability of the Kappa distribution to Coulomb collisions W. Zhang & B. Shizgal
- Thermodynamics of the Inner Heliosheath G. Livadiotis et al.
- Impact of Quantum Non-Locality and Electronic Non-Ideality on the Shannon Entropy for Atomic States in Dense Plasma A. Nuraly et al.
- Complex Systems Methods Characterizing Nonlinear Processes in the Near-Earth Electromagnetic Environment: Recent Advances and Open Challenges G. Balasis et al.
- Kappa-tail Technique: Modeling and Application to Solar Energetic Particles Observed by Parker Solar Probe G. Livadiotis et al.
- Evaluating the Adiabatic Invariants in Magnetized Plasmas Using a Classical Ehrenfest Theorem A. Tamburrini et al.
- Multimode excitation and modulational instability of beam plasma system with Tsallis-distributed electrons P. Bala & T. Gill
- Thermodynamics of Pickup Ions in the Heliosphere G. Livadiotis et al.
- On the origin of the polytropic behavior in space plasmas G. Livadiotis
- Kappa and other nonequilibrium distributions from the Fokker-Planck equation and the relationship to Tsallis entropy B. Shizgal
- Thermodynamic Definitions of Temperature and Kappa and Introduction of the Entropy Defect G. Livadiotis & D. McComas
- Slowing down of charged particles in dusty plasmas with power‐law kappa‐distributions J. Du et al.
- Polytropes in plasmas described by kappa distributions – Application in atmospheric modelling G. Livadiotis
- Long-Term Independence of Solar Wind Polytropic Index on Plasma Flow Speed G. Livadiotis
- Thermodynamic Constraints on Solar Wind Radial Profiles G. Livadiotis & D. McComas
- Blackbody radiation, kappa distribution and superstatistics E. Gravanis & E. Akylas
- Energetic particle distributions in space physics represented by the Pearson differential equation for the kappa distribution B. Shizgal
- The theory of thermodynamic relativity G. Livadiotis & D. McComas
- Universality of kappa distributions G. Livadiotis & D. McComas
- What Defines Stationarity in Space Plasmas G. Livadiotis & D. McComas
- Thermodynamic origin of kappa distributions G. Livadiotis
- Superstatistics from a dynamical perspective: Entropy and relaxation K. Ourabah
- Preface: Nonlinear waves and chaos G. Lakhina et al.
- Kappa Distributions: Statistical Physics and Thermodynamics of Space and Astrophysical Plasmas G. Livadiotis
- Stability of three-dimensional dust acoustic waves in a strongly coupled dusty plasma including kappa distributed superthermal ions and electrons W. El-Taibany et al.
- Anisotropic Kappa Distributions. I. Formulation Based on Particle Correlations G. Livadiotis et al.
- Entropy defect in thermodynamics G. Livadiotis & D. McComas
- Thermal Doppler Broadening of Spectral Emissions in Space and Astrophysical Plasmas G. Livadiotis
- Theoretical aspects of Hamiltonian kappa distributions G. Livadiotis
Saved (final revised paper)
Latest update: 14 May 2026
Short summary
Kappa distributions are frequently used for modeling space plasmas, but their physical origin remains unknown. Recently we realized that the statistical origin of these distributions is not the classical Boltzmann entropy, but the Tsallis q entropy. Thereafter, the question was about the physical origin of this entropic formula. Here we show that the q entropy can be derived under first principles, i.e., by considering that the energy and entropy are additive quantities under certain conditions.
Kappa distributions are frequently used for modeling space plasmas, but their physical origin...
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