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
35 citations as recorded by crossref.
- Forced KdV and Envelope Soliton in Magnetoplasma With Kappa Distributed Ions J. Sarkar et al. https://doi.org/10.1109/TPS.2022.3140318
- Rankine–Hugoniot Shock Conditions for Space and Astrophysical Plasmas Described by Kappa Distributions G. Livadiotis https://doi.org/10.3847/1538-4357/ab487a
- Physical Correlations Lead to Kappa Distributions G. Livadiotis & D. McComas https://doi.org/10.3847/1538-4357/ac99df
- Collision frequency and mean free path for plasmas described by kappa distributions G. Livadiotis https://doi.org/10.1063/1.5125714
- Nonextensive Statistical Mechanics: Equivalence Between Dual Entropy and Dual Probabilities G. Livadiotis https://doi.org/10.3390/e22060594
- Study of ideal gases in curved spacetimes L. Aragón-Muñoz & H. Quevedo https://doi.org/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 https://doi.org/10.1103/PhysRevE.102.062103
- Thermodynamics of the Inner Heliosheath G. Livadiotis et al. https://doi.org/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. https://doi.org/10.3390/e26070602
- Complex Systems Methods Characterizing Nonlinear Processes in the Near-Earth Electromagnetic Environment: Recent Advances and Open Challenges G. Balasis et al. https://doi.org/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. https://doi.org/10.3847/1538-4357/ad5e72
- Evaluating the Adiabatic Invariants in Magnetized Plasmas Using a Classical Ehrenfest Theorem A. Tamburrini et al. https://doi.org/10.3390/e25111559
- Multimode excitation and modulational instability of beam plasma system with Tsallis-distributed electrons P. Bala & T. Gill https://doi.org/10.1007/s12043-021-02080-6
- Thermodynamics of Pickup Ions in the Heliosphere G. Livadiotis et al. https://doi.org/10.3847/1538-4357/ad3e79
- On the origin of the polytropic behavior in space plasmas G. Livadiotis https://doi.org/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 https://doi.org/10.1103/PhysRevE.97.052144
- Thermodynamic Definitions of Temperature and Kappa and Introduction of the Entropy Defect G. Livadiotis & D. McComas https://doi.org/10.3390/e23121683
- Slowing down of charged particles in dusty plasmas with power‐law kappa‐distributions J. Du et al. https://doi.org/10.1002/ctpp.201800046
- Polytropes in plasmas described by kappa distributions – Application in atmospheric modelling G. Livadiotis https://doi.org/10.1002/ctpp.202000041
- Long-Term Independence of Solar Wind Polytropic Index on Plasma Flow Speed G. Livadiotis https://doi.org/10.3390/e20100799
- Thermodynamic Constraints on Solar Wind Radial Profiles G. Livadiotis & D. McComas https://doi.org/10.3847/1538-4357/adea44
- Blackbody radiation, kappa distribution and superstatistics E. Gravanis & E. Akylas https://doi.org/10.1016/j.physa.2021.126132
- Energetic particle distributions in space physics represented by the Pearson differential equation for the kappa distribution B. Shizgal https://doi.org/10.1007/s10509-021-03956-0
- The theory of thermodynamic relativity G. Livadiotis & D. McComas https://doi.org/10.1038/s41598-024-72779-0
- Universality of kappa distributions G. Livadiotis & D. McComas https://doi.org/10.1209/0295-5075/ad4415
- What Defines Stationarity in Space Plasmas G. Livadiotis & D. McComas https://doi.org/10.3847/1538-4357/adb8d2
- Thermodynamic origin of kappa distributions G. Livadiotis https://doi.org/10.1209/0295-5075/122/50001
- Superstatistics from a dynamical perspective: Entropy and relaxation K. Ourabah https://doi.org/10.1103/PhysRevE.109.014127
- Preface: Nonlinear waves and chaos G. Lakhina et al. https://doi.org/10.5194/npg-25-477-2018
- Kappa Distributions: Statistical Physics and Thermodynamics of Space and Astrophysical Plasmas G. Livadiotis https://doi.org/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. https://doi.org/10.1140/epjp/i2019-12888-2
- Anisotropic Kappa Distributions. I. Formulation Based on Particle Correlations G. Livadiotis et al. https://doi.org/10.3847/1538-4365/abd4ed
- Entropy defect in thermodynamics G. Livadiotis & D. McComas https://doi.org/10.1038/s41598-023-36080-w
- Thermal Doppler Broadening of Spectral Emissions in Space and Astrophysical Plasmas G. Livadiotis https://doi.org/10.3847/1538-4365/aae835
- Theoretical aspects of Hamiltonian kappa distributions G. Livadiotis https://doi.org/10.1088/1402-4896/ab12ab
35 citations as recorded by crossref.
- Forced KdV and Envelope Soliton in Magnetoplasma With Kappa Distributed Ions J. Sarkar et al. https://doi.org/10.1109/TPS.2022.3140318
- Rankine–Hugoniot Shock Conditions for Space and Astrophysical Plasmas Described by Kappa Distributions G. Livadiotis https://doi.org/10.3847/1538-4357/ab487a
- Physical Correlations Lead to Kappa Distributions G. Livadiotis & D. McComas https://doi.org/10.3847/1538-4357/ac99df
- Collision frequency and mean free path for plasmas described by kappa distributions G. Livadiotis https://doi.org/10.1063/1.5125714
- Nonextensive Statistical Mechanics: Equivalence Between Dual Entropy and Dual Probabilities G. Livadiotis https://doi.org/10.3390/e22060594
- Study of ideal gases in curved spacetimes L. Aragón-Muñoz & H. Quevedo https://doi.org/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 https://doi.org/10.1103/PhysRevE.102.062103
- Thermodynamics of the Inner Heliosheath G. Livadiotis et al. https://doi.org/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. https://doi.org/10.3390/e26070602
- Complex Systems Methods Characterizing Nonlinear Processes in the Near-Earth Electromagnetic Environment: Recent Advances and Open Challenges G. Balasis et al. https://doi.org/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. https://doi.org/10.3847/1538-4357/ad5e72
- Evaluating the Adiabatic Invariants in Magnetized Plasmas Using a Classical Ehrenfest Theorem A. Tamburrini et al. https://doi.org/10.3390/e25111559
- Multimode excitation and modulational instability of beam plasma system with Tsallis-distributed electrons P. Bala & T. Gill https://doi.org/10.1007/s12043-021-02080-6
- Thermodynamics of Pickup Ions in the Heliosphere G. Livadiotis et al. https://doi.org/10.3847/1538-4357/ad3e79
- On the origin of the polytropic behavior in space plasmas G. Livadiotis https://doi.org/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 https://doi.org/10.1103/PhysRevE.97.052144
- Thermodynamic Definitions of Temperature and Kappa and Introduction of the Entropy Defect G. Livadiotis & D. McComas https://doi.org/10.3390/e23121683
- Slowing down of charged particles in dusty plasmas with power‐law kappa‐distributions J. Du et al. https://doi.org/10.1002/ctpp.201800046
- Polytropes in plasmas described by kappa distributions – Application in atmospheric modelling G. Livadiotis https://doi.org/10.1002/ctpp.202000041
- Long-Term Independence of Solar Wind Polytropic Index on Plasma Flow Speed G. Livadiotis https://doi.org/10.3390/e20100799
- Thermodynamic Constraints on Solar Wind Radial Profiles G. Livadiotis & D. McComas https://doi.org/10.3847/1538-4357/adea44
- Blackbody radiation, kappa distribution and superstatistics E. Gravanis & E. Akylas https://doi.org/10.1016/j.physa.2021.126132
- Energetic particle distributions in space physics represented by the Pearson differential equation for the kappa distribution B. Shizgal https://doi.org/10.1007/s10509-021-03956-0
- The theory of thermodynamic relativity G. Livadiotis & D. McComas https://doi.org/10.1038/s41598-024-72779-0
- Universality of kappa distributions G. Livadiotis & D. McComas https://doi.org/10.1209/0295-5075/ad4415
- What Defines Stationarity in Space Plasmas G. Livadiotis & D. McComas https://doi.org/10.3847/1538-4357/adb8d2
- Thermodynamic origin of kappa distributions G. Livadiotis https://doi.org/10.1209/0295-5075/122/50001
- Superstatistics from a dynamical perspective: Entropy and relaxation K. Ourabah https://doi.org/10.1103/PhysRevE.109.014127
- Preface: Nonlinear waves and chaos G. Lakhina et al. https://doi.org/10.5194/npg-25-477-2018
- Kappa Distributions: Statistical Physics and Thermodynamics of Space and Astrophysical Plasmas G. Livadiotis https://doi.org/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. https://doi.org/10.1140/epjp/i2019-12888-2
- Anisotropic Kappa Distributions. I. Formulation Based on Particle Correlations G. Livadiotis et al. https://doi.org/10.3847/1538-4365/abd4ed
- Entropy defect in thermodynamics G. Livadiotis & D. McComas https://doi.org/10.1038/s41598-023-36080-w
- Thermal Doppler Broadening of Spectral Emissions in Space and Astrophysical Plasmas G. Livadiotis https://doi.org/10.3847/1538-4365/aae835
- Theoretical aspects of Hamiltonian kappa distributions G. Livadiotis https://doi.org/10.1088/1402-4896/ab12ab
Saved (final revised paper)
Latest update: 15 Jul 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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