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Global statistical entropy and its implications for the main sequences of stars and galaxies

David Elbaz

TL;DR

The paper addresses how the second law of thermodynamics applies to cosmic evolution when radiation is included by defining a global entropy S_global = S_part + S_photons, with the photon contribution given by S_photons ≈ 3.6 k_B N_photons. Using the fluctuation theorem P_2/P_1 = exp(ΔS/k_B), the author argues that stars on the main sequence converge to a universal specific entropy production per unit mass, and galaxies on the star-formation main sequence show a similar universality, both driven by photon production rather than nuclear fusion entropy. Structure formation is interpreted as entropy maximization via energy-to-photon slicing, with the cosmic background revealing the dominance of long-wavelength photons in entropy production (CIB vs COB). The analysis further suggests that living systems, exemplified by humans, produce entropy per unit mass and time far more efficiently than stars, hinting that life may be a thermodynamically favored outcome in the Universe, though the argument remains probabilistic. Overall, the work provides a thermodynamic lens linking cosmic structure, radiation, and the potential prevalence of life through universal entropy production pathways.

Abstract

In a dissipative system such as star or a galaxy, the emitted photons are decoupled from matter particles and may therefore be considered as part of a closed system to which the Second Law of Thermodynamics applies. In the present paper, we define a global entropy using a statistical approach that accounts for the contributions of both matter particles and photons. The statistical contribution of radiation is described as a photon gas in the definition of this global entropy. The increase in global entropy can foster structure formation -- rather than disorder -- because structures such as stars and galaxies are efficient at dissipating energy in the form of photons, and thus at producing entropy. We show that stars generate a nearly equal amount of specific entropy, and therefore a comparable number of photons per unit mass, over their lifetime on the main sequence of the Hertzsprung-Russell (HR) diagram. This suggests that the main sequence of the HR diagram constitutes a locus of convergence toward a universal specific entropy production by stars. We then examine the implications of this approach for the star-formation main sequence in galaxies, and find a similar result. The emergence of organized structures in cosmic history reflects the second law, as organized matter is efficient at generating entropy through the slicing of energy into lower-frequency photons. This is also reflected in the dominant contribution of low-frequency photons to the extragalactic background light. Finally, we briefly discuss how this perspective may inform us on the possibility of the existence of life elsewhere in the universe.

Global statistical entropy and its implications for the main sequences of stars and galaxies

TL;DR

The paper addresses how the second law of thermodynamics applies to cosmic evolution when radiation is included by defining a global entropy S_global = S_part + S_photons, with the photon contribution given by S_photons ≈ 3.6 k_B N_photons. Using the fluctuation theorem P_2/P_1 = exp(ΔS/k_B), the author argues that stars on the main sequence converge to a universal specific entropy production per unit mass, and galaxies on the star-formation main sequence show a similar universality, both driven by photon production rather than nuclear fusion entropy. Structure formation is interpreted as entropy maximization via energy-to-photon slicing, with the cosmic background revealing the dominance of long-wavelength photons in entropy production (CIB vs COB). The analysis further suggests that living systems, exemplified by humans, produce entropy per unit mass and time far more efficiently than stars, hinting that life may be a thermodynamically favored outcome in the Universe, though the argument remains probabilistic. Overall, the work provides a thermodynamic lens linking cosmic structure, radiation, and the potential prevalence of life through universal entropy production pathways.

Abstract

In a dissipative system such as star or a galaxy, the emitted photons are decoupled from matter particles and may therefore be considered as part of a closed system to which the Second Law of Thermodynamics applies. In the present paper, we define a global entropy using a statistical approach that accounts for the contributions of both matter particles and photons. The statistical contribution of radiation is described as a photon gas in the definition of this global entropy. The increase in global entropy can foster structure formation -- rather than disorder -- because structures such as stars and galaxies are efficient at dissipating energy in the form of photons, and thus at producing entropy. We show that stars generate a nearly equal amount of specific entropy, and therefore a comparable number of photons per unit mass, over their lifetime on the main sequence of the Hertzsprung-Russell (HR) diagram. This suggests that the main sequence of the HR diagram constitutes a locus of convergence toward a universal specific entropy production by stars. We then examine the implications of this approach for the star-formation main sequence in galaxies, and find a similar result. The emergence of organized structures in cosmic history reflects the second law, as organized matter is efficient at generating entropy through the slicing of energy into lower-frequency photons. This is also reflected in the dominant contribution of low-frequency photons to the extragalactic background light. Finally, we briefly discuss how this perspective may inform us on the possibility of the existence of life elsewhere in the universe.
Paper Structure (13 sections, 28 equations, 3 figures)

This paper contains 13 sections, 28 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Global entropy of dissipative systems and structure formation in the Universe
  3. Definition of the global entropy
  4. The fluctuation theorem
  5. Implications of the global entropy and second law on cosmic structures
  6. Universality of the global entropy produced by stars during their lifetime on the MS
  7. Universality of the global entropy produced by star-forming galaxies on the SFMS
  8. Global entropy and the cosmic background
  9. The second law and the emergence of life
  10. Conclusion
  11. Entropy of a gas of photons
  12. Global entropy produced by a star
  13. Comparison of the specific entropy generated by a star and a living body

Figures (3)

  • Figure 1: Comparison of specific luminosity (dashed line), specific entropy production (dash-dotted line), and specific entropy production integrated over the lifetime of a star on the MS of the HR diagram (solid blue line) for stars of different masses. All curves are normalized to a value of one at the mass of the Sun.
  • Figure 2: Comparison of specific entropy production integrated over the lifetime of a star on the MS of the HR diagram (solid blue line) for stars of different masses (normalized to unity for a solar-mass star) with the specific entropy production of galaxies on the SFMS for galaxies of different masses (dashed red line; upper horizontal axis). The normalization of the SFMS evolves with redshift; here, it is normalized to unity at 10$^9$ M$_{\odot}$.
  • Figure 3: Extragalactic background light generated by star formation in galaxies since cosmic dawn (solid lines), shown in blue on the optical side and as a red line in the infrared, where stellar light is reprocessed by dust (data from lagache2005). The dashed lines show the relative amount of entropy, traced by the number of photons, that has accumulated and been carried by photons throughout the history of star formation in galaxies.