This chapter covers a period in which Boltzmann returned to the collision-based approach and consolidated it in answer to criticism and suggestions by William Thomson, Hendrik Lorentz, George Bryan, Gustav Kirchhoff, and Max Planck. He corrected errors in alleged counterexamples of equipartition by William Burnside and William Thomson; and in 1887, when the Dutch theorist Hendrik Lorentz detected an error in his earlier derivation of the H theorem for polyatomic gases, he devised a highly ingenious alternative. In 1894, he offered a new, simplified derivation of the Maxwell–Boltzmann distribution based on an idea by the British mathematician George Bryan. Together with Bryan, he also provided a kinetic-molecular model for the equalization of the temperatures of two contiguous gases. He denounced what he believed to be an error in Gustav Kirchhoff’s derivation of Maxwell’s distribution, and he strengthened Max Planck’s alternative derivation based on time reversal.
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