The Second Law of Thermodynamics: Mathematical Error

Details The Second Law of Thermodynamics: Mathematical Error The Second Law of Thermodynamics: Mathematical Error

Apr 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006aps..apr.d1056k&link_type=abstract

American Physical Society, APS April Meeting, April 22-26, 2006, abstract #D1.056

Mathematics

Probability

Scientific paper

The critical analysis of the generally accepted foundations of thermodynamics is proposed. Within the framework of the work [1], the following statement is proved: Gibbs's quantum canonical distribution fn =f0 exp (-{En } / {{En } {T)}}} {T)} (whereEn , n=0,;1,;... , fn , T are the energy of the subsystem, probability, and temperature, respectively) defines the correct relation of the thermal energy Q of the subsystem to the entropy S of the subsystem and the temperature T. This relation has the form: S=Q / {Q T}} } T and {lim }limits {T-> 0 } S=0 (where Q≡ ∑ limits n=0∞ {En } fn , S≡ ∑ limits n=0∞ {Sn fn } , Sn ≡ {En } / {{En } {T=-ln ({fn } / {{fn } {f0 )}}} {f0 )}}}} {T=-ln ({fn } {{fn } {f0 )}}} {f0 )}}). Consequence: the second law (i.e. dS={dQ} / {{dQ} T}}. (T) of thermodynamics represents mathematical error. Ref.: [1] T.Z. Kalanov, ``On the main errors underlying statistical physics.'' Bulletin of the APS, Vol. 47, No. 2 (2005), p. 164.

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