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.
Review article
| 
07 Feb 2018
Review article |
| 07 Feb 2018
| 07 Feb 2018
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
34 citations as recorded by crossref.
- Forced KdV and Envelope Soliton in Magnetoplasma With Kappa Distributed Ions J. Sarkar et al. 10.1109/TPS.2022.3140318
- Rankine–Hugoniot Shock Conditions for Space and Astrophysical Plasmas Described by Kappa Distributions G. Livadiotis 10.3847/1538-4357/ab487a
- Physical Correlations Lead to Kappa Distributions G. Livadiotis & D. McComas 10.3847/1538-4357/ac99df
- Collision frequency and mean free path for plasmas described by kappa distributions G. Livadiotis 10.1063/1.5125714
- Nonextensive Statistical Mechanics: Equivalence Between Dual Entropy and Dual Probabilities G. Livadiotis 10.3390/e22060594
- Study of ideal gases in curved spacetimes L. Aragón-Muñoz & H. Quevedo 10.1142/S0219887823501505
- 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 10.1103/PhysRevE.102.062103
- Thermodynamics of the Inner Heliosheath G. Livadiotis et al. 10.3847/1538-4365/ac8b88
- Impact of Quantum Non-Locality and Electronic Non-Ideality on the Shannon Entropy for Atomic States in Dense Plasma A. Nuraly et al. 10.3390/e26070602
- Complex Systems Methods Characterizing Nonlinear Processes in the Near-Earth Electromagnetic Environment: Recent Advances and Open Challenges G. Balasis et al. 10.1007/s11214-023-00979-7
- Kappa-tail Technique: Modeling and Application to Solar Energetic Particles Observed by Parker Solar Probe G. Livadiotis et al. 10.3847/1538-4357/ad5e72
- Evaluating the Adiabatic Invariants in Magnetized Plasmas Using a Classical Ehrenfest Theorem A. Tamburrini et al. 10.3390/e25111559
- Multimode excitation and modulational instability of beam plasma system with Tsallis-distributed electrons P. Bala & T. Gill 10.1007/s12043-021-02080-6
- Thermodynamics of Pickup Ions in the Heliosphere G. Livadiotis et al. 10.3847/1538-4357/ad3e79
- On the origin of the polytropic behavior in space plasmas G. Livadiotis 10.1088/1742-6596/1332/1/012010
- Kappa and other nonequilibrium distributions from the Fokker-Planck equation and the relationship to Tsallis entropy B. Shizgal 10.1103/PhysRevE.97.052144
- Thermodynamic Definitions of Temperature and Kappa and Introduction of the Entropy Defect G. Livadiotis & D. McComas 10.3390/e23121683
- Slowing down of charged particles in dusty plasmas with power‐law kappa‐distributions J. Du et al. 10.1002/ctpp.201800046
- Polytropes in plasmas described by kappa distributions – Application in atmospheric modelling G. Livadiotis 10.1002/ctpp.202000041
- Long-Term Independence of Solar Wind Polytropic Index on Plasma Flow Speed G. Livadiotis 10.3390/e20100799
- Blackbody radiation, kappa distribution and superstatistics E. Gravanis & E. Akylas 10.1016/j.physa.2021.126132
- Energetic particle distributions in space physics represented by the Pearson differential equation for the kappa distribution B. Shizgal 10.1007/s10509-021-03956-0
- The theory of thermodynamic relativity G. Livadiotis & D. McComas 10.1038/s41598-024-72779-0
- Universality of kappa distributions G. Livadiotis & D. McComas 10.1209/0295-5075/ad4415
- What Defines Stationarity in Space Plasmas G. Livadiotis & D. McComas 10.3847/1538-4357/adb8d2
- Thermodynamic origin of kappa distributions G. Livadiotis 10.1209/0295-5075/122/50001
- Superstatistics from a dynamical perspective: Entropy and relaxation K. Ourabah 10.1103/PhysRevE.109.014127
- Preface: Nonlinear waves and chaos G. Lakhina et al. 10.5194/npg-25-477-2018
- Kappa Distributions: Statistical Physics and Thermodynamics of Space and Astrophysical Plasmas G. Livadiotis 10.3390/universe4120144
- 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. 10.1140/epjp/i2019-12888-2
- Anisotropic Kappa Distributions. I. Formulation Based on Particle Correlations G. Livadiotis et al. 10.3847/1538-4365/abd4ed
- Entropy defect in thermodynamics G. Livadiotis & D. McComas 10.1038/s41598-023-36080-w
- Thermal Doppler Broadening of Spectral Emissions in Space and Astrophysical Plasmas G. Livadiotis 10.3847/1538-4365/aae835
- Theoretical aspects of Hamiltonian kappa distributions G. Livadiotis 10.1088/1402-4896/ab12ab
34 citations as recorded by crossref.
- Forced KdV and Envelope Soliton in Magnetoplasma With Kappa Distributed Ions J. Sarkar et al. 10.1109/TPS.2022.3140318
- Rankine–Hugoniot Shock Conditions for Space and Astrophysical Plasmas Described by Kappa Distributions G. Livadiotis 10.3847/1538-4357/ab487a
- Physical Correlations Lead to Kappa Distributions G. Livadiotis & D. McComas 10.3847/1538-4357/ac99df
- Collision frequency and mean free path for plasmas described by kappa distributions G. Livadiotis 10.1063/1.5125714
- Nonextensive Statistical Mechanics: Equivalence Between Dual Entropy and Dual Probabilities G. Livadiotis 10.3390/e22060594
- Study of ideal gases in curved spacetimes L. Aragón-Muñoz & H. Quevedo 10.1142/S0219887823501505
- 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 10.1103/PhysRevE.102.062103
- Thermodynamics of the Inner Heliosheath G. Livadiotis et al. 10.3847/1538-4365/ac8b88
- Impact of Quantum Non-Locality and Electronic Non-Ideality on the Shannon Entropy for Atomic States in Dense Plasma A. Nuraly et al. 10.3390/e26070602
- Complex Systems Methods Characterizing Nonlinear Processes in the Near-Earth Electromagnetic Environment: Recent Advances and Open Challenges G. Balasis et al. 10.1007/s11214-023-00979-7
- Kappa-tail Technique: Modeling and Application to Solar Energetic Particles Observed by Parker Solar Probe G. Livadiotis et al. 10.3847/1538-4357/ad5e72
- Evaluating the Adiabatic Invariants in Magnetized Plasmas Using a Classical Ehrenfest Theorem A. Tamburrini et al. 10.3390/e25111559
- Multimode excitation and modulational instability of beam plasma system with Tsallis-distributed electrons P. Bala & T. Gill 10.1007/s12043-021-02080-6
- Thermodynamics of Pickup Ions in the Heliosphere G. Livadiotis et al. 10.3847/1538-4357/ad3e79
- On the origin of the polytropic behavior in space plasmas G. Livadiotis 10.1088/1742-6596/1332/1/012010
- Kappa and other nonequilibrium distributions from the Fokker-Planck equation and the relationship to Tsallis entropy B. Shizgal 10.1103/PhysRevE.97.052144
- Thermodynamic Definitions of Temperature and Kappa and Introduction of the Entropy Defect G. Livadiotis & D. McComas 10.3390/e23121683
- Slowing down of charged particles in dusty plasmas with power‐law kappa‐distributions J. Du et al. 10.1002/ctpp.201800046
- Polytropes in plasmas described by kappa distributions – Application in atmospheric modelling G. Livadiotis 10.1002/ctpp.202000041
- Long-Term Independence of Solar Wind Polytropic Index on Plasma Flow Speed G. Livadiotis 10.3390/e20100799
- Blackbody radiation, kappa distribution and superstatistics E. Gravanis & E. Akylas 10.1016/j.physa.2021.126132
- Energetic particle distributions in space physics represented by the Pearson differential equation for the kappa distribution B. Shizgal 10.1007/s10509-021-03956-0
- The theory of thermodynamic relativity G. Livadiotis & D. McComas 10.1038/s41598-024-72779-0
- Universality of kappa distributions G. Livadiotis & D. McComas 10.1209/0295-5075/ad4415
- What Defines Stationarity in Space Plasmas G. Livadiotis & D. McComas 10.3847/1538-4357/adb8d2
- Thermodynamic origin of kappa distributions G. Livadiotis 10.1209/0295-5075/122/50001
- Superstatistics from a dynamical perspective: Entropy and relaxation K. Ourabah 10.1103/PhysRevE.109.014127
- Preface: Nonlinear waves and chaos G. Lakhina et al. 10.5194/npg-25-477-2018
- Kappa Distributions: Statistical Physics and Thermodynamics of Space and Astrophysical Plasmas G. Livadiotis 10.3390/universe4120144
- 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. 10.1140/epjp/i2019-12888-2
- Anisotropic Kappa Distributions. I. Formulation Based on Particle Correlations G. Livadiotis et al. 10.3847/1538-4365/abd4ed
- Entropy defect in thermodynamics G. Livadiotis & D. McComas 10.1038/s41598-023-36080-w
- Thermal Doppler Broadening of Spectral Emissions in Space and Astrophysical Plasmas G. Livadiotis 10.3847/1538-4365/aae835
- Theoretical aspects of Hamiltonian kappa distributions G. Livadiotis 10.1088/1402-4896/ab12ab
Discussed (final revised paper)
Latest update: 14 Jul 2025
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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