![]() ![]() (See also PHYSICS TODAY, January 1992, page 44, for a marvelous description by Boltzmann of his visit to California in 1906. According to the Boltzmann equation, entropy is a measure of the number of microstates available to a system. for further reading I highly recommend Boltzmann's works as well as references 2–7. The generalized entropyor relative entropy. All claims of inconsistencies that I know of are, in my opinion, wrong I see no need for alternate explanations. The object of the paper is to generalize Boltzmann entropy to takeaccount of the subjective nature of a system. Entropy for a general probability distribution and Boltzmann distribution. Deriving the partition function in Ma圎nt. 9.2 Boltzmann's Entropy Analogs Boltzmann 1872 presented an analog for the entropy in the form of the logarithm of the one - particle probability. In Erwin Schrödinger's words, “Boltzmann's ideas really give an understanding” of the origin of macroscopic behavior. Deriving Boltzmann statistics from the maximum entropy principle. Since next year, 1994, is the 150th anniversary of Boltzmann's birth, this is a fitting moment to review his ideas on the arrow of time. For an irreversible process the entropy increases. Thus Boltzmann never encounters the apparent Gibbs paradox for the entropy of mixing of identical gases. The entropy and the number of microstates of a specific system are connected through the Boltzmann’s entropy equation (1896): k ln W 2nd Law of Termodynamics: S 0 For a closed system, entropy can only increase, it can never decrease. Crucially, is an extensive quantity, which leads to Boltzmann’s extensive Equation (62) for the entropy of an ideal gas. There is really no excuse for this, considering the clarity of Boltzmann's later writings. Confusingly, Planck later chose to write Boltzmann’s equation for entropy as SklnW+constant. The entropy and the number of microstates of a specific system are connected through the Boltzmann’s entropy equation (1896): k ln W. The controversies generated by the misunderstandings of Ernst Zermelo and others have been perpetuated by various authors. (See figure 1.) I attribute this confusion to the originality of Boltzmann's ideas: It made them difficult for some of his contemporaries to grasp. Given the success of Ludwig Boltzmann's statistical approach in explaining the observed irreversible behavior of macroscopic systems in a manner consistent with their reversible microscopic dynamics, it is quite surprising that there is still so much confusion about the problem of irreversibility.
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