Astronomy and Astrophysics – Astrophysics
Scientific paper
Apr 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002aps..apro12010k&link_type=abstract
American Physical Society, April Meeting, Jointly Sponsored with the High Energy Astrophysics Division (HEAD) of the American As
Astronomy and Astrophysics
Astrophysics
Scientific paper
The basis of statistical physics that was created by Maxwell, Boltzmann, Gibbs, Planck, Bose, Einstein, Fermi has been analyzed critically. The analysis is based on the concepts of discrete accidental quantity (the energy of the subsystem), statistical ensemble of identical systems and temperature. The key idea is that the expression for the distribution function (giving the complete quantum-statistical description of a subsystem) is the equation for the universal parameter the temperature T of the subsystems; in view of logic, the solution of the equation presents the quantum-statistical definition of T; the T is to characterize the empirically found general property of thermal processes (i.e., the T is not to depend on the structure of the energy spectrum of the subsystem). The results of the critical analysis are, in particular, as follows. (1) The energy of the subsystem must be counted off its least value. (2) The range of the parameter T of the subsystem is given by 0 < T < E_∞ where E_∞ is the boundary of the energy spectrum of the subsystem. If T = 0, then the description of the subsystem loses its statistical meaning because, in this case, the energy of the subsystem is not an accidental quantity (hence, the thermal energy of this subsystem equals zero). (3) The Boltzmann formula S = klogW, the Boltzmann-Gibbs and Einstein-Planck formulae for entropy S are incorrect. (4) The correct expression for the entropy of the subsystem has the form S = sumnolimitsn = 0^∞ S_nf_n, Sn ≡ E_n/T = - ln(f_n/f_0), n = 0, 1, ldots where E_n, fn are the energy of the subsystem and the Gibbs quantum canonical distribution, respectively. In the thermodynamical limit, S = 1 (therefore, thermodynamics should be corrected). (5) The Gibbs grand-canonical distribution, the Bose-Einstein and Fermi-Dirac distribution functions are incorrect because they contain the chemical potential μ. (6) The Einstein coefficients A_nm, B_nm, B_mn are different from zero only if A_nm ≡ B_nm ≡ B_mn ≡ P_nm^10 (where P_nm^q + 1, q is the (m, q) arrow (n, q + 1) transition probability in unit time; the quantum numbers q, q + 1 and m, n characterize the energetic states of the photon gas and of the molecule, respectively). Thus, the generally accepted basis of statistical physics includes the essential errors that are due to violation of the laws of logic. Correction of the errors open a way to unitarization of the principles of statistical physics and physical kinetics. (A more detailed consideration is given in a dissertation [T.Z.Kalanov, “The correct quantum-statistical description of the ideal systems within the framework of the master equation”, Tashkent, 1993]).
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