Ludwig Boltzmann
1844-1906
Born 1844 in Vienna, Austria. Ph.D. from the University of Vienna, 1866. Tought at the University of Graz, 1869-72. Professor of Mathematics, University of Vienna, 1873-75, then Professor of Experimental Physics at Graz, 1876-89. Subsequently Professor of Theoretical Physics at Munich, 1890-95, Vienna, 1895-1900, and Leipzig, 1900-02, and Vienna again.
First work on the mechanization of the second law of thermodynamics, 1866. Introduced Boltzmann distribution in 1868 for particles in a field, generalizing Maxwell's 1859, 1867 velocity distribution. Used kinetic methods, statistical ideas applied to gases, introduced the concept of thermodynamic probabilities. Derived the general Boltzmann distribution including particle interactions, 1871. Introduced the idea of statistical ensembles, proved the equipartition of energy, 1871. Introduced the Boltzmann transport equation, stated the H theorem and studied the approach to equilibrium statistically, 1872. Developed the general H theorem, 1876. Introduced purely statistical methods, Boltzmann statistics, developed the relation of entropy to the statistical weights W of configurations, 1877. Derived the Stefan-Boltzmann law for black body radiation, 1884.
Boltzmann's ideas were highly controversial, and were opposed by the "energeticists," including Mach and Ostwald. He was an outstanding lecturer, but his scientific papers tended to be long and dense, and caused problems even for such people as Maxwell. The very subtle H theorem, which appears to contradict microscopic reversibility in mechanics if improperly interpreted, as pointed out by Loschmidt, led to protracted controversies with Zermelo and others. The subtleties were ultimately explained by Paul and Tatyana Afanassjewa Ehrenfest by example in 1906 and in detail in 1911. (Paul Ehrenfest had been a student of Boltzmann's. Tatyana was a mathematician.) The failure of Boltzmann's ideas to gain acceptance led to depression and his suicide in 1906. They were established experimentally in the context of Brownian motion by Perrin in 1908 following Einstein's 1905 work.
Boltzmann's epitaph in the Central Cemetary in Vienna reads
Ludwig Boltzmann
1844-1906
S = k lnW