Abstract
Why does Planck (1900), referring to Boltzmann’s 1877 probabilistic treatment, obtain his quantum distribution function while Boltzmann did not? To answer this question, both treatments are compared on the basis of Boltzmann’s 1868 three-level scheme (configuration—occupation—occupancy). Some calculations by Planck (1900, 1901, and 1913) and Einstein (1907) are also sketched. For obtaining a quantum distribution, it is crucial to stick with a discrete energy spectrum and to make the limit transitions to infinity at the right place. For correct state counting, the concept of interchangeability of particles is superior to that of indistinguishability.
Highlights
Very recently, Sharp and Matschinsky have translated and commented Boltzmann’s famous 1877 paper [1] “On the Relationship between the Second Fundamental Theorem of the Mechanical Theory of Heat and Probability Calculations regarding the Conditions for Thermal Equilibrium” [2]
Any of Boltzmann’s original scientific work is available in translation. This is remarkable given his central role in the development of both equilibrium and non-equilibrium statistical mechanics, his statistical mechanical explanation of entropy, and our understanding of the Second Law of thermodynamics
On the contrary, phenomenological thermodynamics, classical statistics, and quantum statistics are all in just the same logical position with regard to extensivity of entropy; they are silent on the issue, neither requiring it nor forbidding it.”
Summary
Sharp and Matschinsky have translated and commented Boltzmann’s famous 1877 paper [1] “On the Relationship between the Second Fundamental Theorem of the Mechanical Theory of Heat and Probability Calculations regarding the Conditions for Thermal Equilibrium” [2]. Any of Boltzmann’s original scientific work is available in translation This is remarkable given his central role in the development of both equilibrium and non-equilibrium statistical mechanics, his statistical mechanical explanation of entropy, and our understanding of the Second Law of thermodynamics. . .Gibbs [in “Heterogeneous Equilibrium”] displays a full understanding of this problem, and disposes of it without a trace of that confusion over the “meaning of entropy” or “operational distinguishability of particles” on which later writers have stumbled He goes straight to the heart of the matter as a simple technical detail, understood as soon as one has grasped the full meanings of the words “state” and “reversible” as they are used in thermodynamics. Einstein concludes quantization to be a selection problem of states
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