سوال ۲۴ کنکور ارشد فیزیک ۱۴۰۳

PART C: Reading Comprehension — PASSAGE 3

[1] When Einstein’s great papers of 1905 appeared in print, he was not a newcomer to the Annalen der Physik, in which he published most of his early works. Of crucial importance for his further research were three early papers on the foundations of statistical mechanics, in which he tried to fill what he considered to be a gap in the mechanical foundations of thermodynamics. When Einstein wrote his three papers he was not familiar with the work of Gibbs and only partially with that of Boltzmann. [2] Einstein’s papers, like Gibbs’s Elementary Principles of Statistical Mechanics of 1902, form a bridge between Boltzmann’s work and the modern approach to statistical mechanics. In particular, Einstein independently formulated the distinction between the microcanonical and canonical ensembles and derived the equilibrium distribution for the canonical ensemble from the microcanonical distribution. [3]

Einstein’s profound insight into the nature and size of fluctuations played a decisive role for his most revolutionary contribution to physics: the light-quantum hypothesis. [4] Indeed, Einstein extracted the light-quantum postulate from a statistical-mechanical analogy between radiation in the Wien regime and a classical ideal gas of material particles. In this consideration, Boltzmann’s principle, relating entropy and probability of macroscopic states, played a key role. Later Einstein extended these considerations to an analysis of energy and momentum fluctuations in the radiation field.

24- In which position marked by [1], [2], [3] or [4], can the following sentence best be inserted in the passage?

Of special importance for his later research was the derivation of the energy-fluctuation formula for the canonical ensemble.