Tomaschitz, R.
(2016). Partition function and thermodynamic parameters of the all-particle
cosmic-ray flux, *Astroparticle Physics ***84**, 36–51, DOI:
10.1016/j.astropartphys.2016.08.003

**Abstract (**ScienceDirect**, **SAO/NASA ADS**)**

The all-particle
cosmic-ray energy spectrum is studied in the 1 GeV–10^{11} GeV
interval, the relativistic nuclei being treated as a free multi-component gas
in stationary non-equilibrium. A phase-space derivation of the spectral number
density, partition function and entropy is given, and an analytic expression
for the flux density of the all-particle spectrum is semi-empirically obtained
from a wideband spectral fit. The all-particle spectrum is the additive superposition
of four strongly overlapping peaks with exponential cutoffs at the spectral
breaks. The analytic flux density covers the mentioned interval ranging over
eleven decades and accurately reproduces the spectral fine-structure, such as
two weak spectral breaks between knee and ankle emerging in the IceTop-73 and
KASCADE-Grande data sets. In the low-energy range below 10^{4} GeV, the
all-particle flux is approximated by adding the proton and helium flux
densities obtained from fits to the AMS-02 and CREAM spectra, the contribution
of heavier nuclei being negligible in this energy range. Estimates of the
thermodynamic parameters (number count, internal energy, entropy and pressure)
of the all-particle flux and the partial fluxes generating the spectral peaks
are derived.

05.20.Gg Classical ensemble theory

05.30.Ch Quantum ensemble theory

05.70.Ce Thermodynamic functions and equations of state

98.70.Sa Cosmic rays

description: Roman
Tomaschitz (2016) Partition function and thermodynamic parameters of the
all-particle cosmic-ray flux, *Astropart.* *Phys. ***84**, 36.

**Keywords:** Spectral breaks in the all-particle cosmic-ray flux;
Wideband spectral fits with multiplicative flux densities; Decomposition of
wideband spectra into spectral peaks; Partition function of relativistic
stationary non-equilibrium ensembles; Entropy of cosmic-ray nuclei; Flux
densities of proton and helium spectra

**Highlights**

The all-particle cosmic-ray spectrum is generated by the flux density of a stationary non-equilibrium gas of relativistic nuclei.

Reconstruction of
the phase-space probability distribution and partition function from wideband
spectral fits in the 1 GeV–10^{11} GeV interval.

An analytic expression for the spectral flux density is obtained, exhibiting two weak spectral breaks between knee and ankle.

Decomposition of the all-particle energy spectrum into four exponentially decaying spectral peaks with crossovers at the spectral breaks.

Thermodynamic parameters of cosmic-ray fluxes: temperature, specific number, energy and entropy densities, pressure.

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