The second law of thermodynamics - No process is possible, the sole result of which is that heat is transferred from a body to a hotter one (Clausius)[1]. Black-hole physics mirrors thermodynamics in many respects. The formal black hole analog of the ordinary second law of thermodynamics (OSL), "the entropy of a closed system never decreases," is Hawking's theorem, "the surface area of a black hole never decreases."[2].
The law of black body radiation - A blackbody is an equilibrium object with an absorption coefficient and radiation coefficient of 1 for light. A blackbody is a substance made up of fermions, which are the only ones that can absorb photons; due to the vibrations of the material particle equivalent oscillator*, a blackbody radiates bosons, photons. Thus, a blackbody can be regarded as a mixed system of fermions and bosons. The radiation spectrum of a blackbody obeys Planck's Law of Radiation (Stefan-Boltzmann Law of Radiation, Wien's Displacement Law)[3][4][5] and is related to the temperature T only. The study of blackbody radiation yielded the earliest quantum hypothesis E = hν [3]**.The cosmic microwave background (CMB) obeys the law of blackbody radiation [6]; Quantum mechanics together with general relativity predicts that a black hole behaves like a black body, emitting thermal radiations, with a temperature proportional to its surface gravity at the black hole horizon and with an entropy proportional to its horizon area [7][8][9].
Bose statistics and Fermi statistics - the cause of the difference in their statistical characteristics lies in the Pauli exclusion principle. Define E(s) = ε(s) - μ(s): the kinetic and potential energy of a free particle in the s-state, Fermi-Dirac Statistics: n_FD = [e^(ε-μ)/KT+1]^-1; Bose-Einstein Statistics: n_BE = [e^(ε-μ)/KT-1]^-1.
The three laws mentioned above, as well as the first law of thermodynamics (conservation of energy), are closely related and determined by each other.
Questions:
1) Suppose there is a closed space full of fermions (assuming some sort of quantum black hole is equivalent) and bosons, where vibrations of fermions produce bosons and bosons are absorbed by fermions. If the amount of energy-momentum contained in this closed system could be changed arbitrarily by some means, what are the absolute limits, minimum and maximum, of the entropy contained therein? What is their significance?
2) Barrow said, "The smallest of all particle masses is likely to be special because the lightest particles can no longer continue to decay - they cannot decay into lighter particles. They will inevitably dominate the universe eventually" [10]. Can we consider the photon to be the limit of all other particle decay? Because it is the only one that has zero mass and never decays. What does this limit of decay mean? Does it correspond in any way to the entropy limit?
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Notes
* Here there is no spontaneous or excited radiation because the radiation spectrum is a continuous spectrum.
** “Probably the most direct support for the fundamental idea of the hypothesis of quanta is supplied by the values of the elementary quanta of matter and electricity derived from it"[3]; Note the close relationship between quanta implied here, which is the most intuitive and purest of observations and associations, as yet undisturbed by subsequent developments in physics.
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References
[1] Lieb, E. H. and J. Yngvason (1998). "A guide to entropy and the second law of thermodynamics." Notices of the AMS 45: 571.
[2] Bekenstein, J. D. (1974). "Generalized second law of thermodynamics in black-hole physics." Physical Review D 9(12): 3292.
[3] Planck, M. (1900). The theory of heat radiation.
[4] Gearhart, C. A. (2002). "Planck, the Quantum, and the Historians." Physics in perspective 4(2): 170-215.
[5] Jain, P. and L. Sharma (1998). "The Physics of blackbody radiation: A review." Journal of Applied Science in Southern Africa 4: 80-101.
[6] PROGRAM, P. "PLANCK PROGRAM." ; "The Wilkinson Microwave Anisotropy Probe (WMAP) ".
[7] Cai, R.-G. and S. P. Kim (2005). "First law of thermodynamics and Friedmann equations of Friedmann-Robertson-Walker universe." Journal of High Energy Physics 2005(02): 050.
[8] Hawking, S. W. (1975). Particle creation by black holes. Euclidean quantum gravity, World Scientific: 167-188.
[9] Almheiri, A., T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini (2021). "The entropy of Hawking radiation." Reviews of Modern Physics 93(3): 035002.
[10] Barrow, J. D., P. C. Davies and C. L. Harper Jr (2004). Science and ultimate reality: Quantum theory, cosmology, and complexity, Cambridge University Press.
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