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BOLTZMANN, Ludwig Eduard

* 20. 2. 1844, Vienna, Austria

† 5. 9. 1906, Duino near Trieste, Italy

physicist, mathematician, scientific theoretician

B.'s father was a county financial commissioner in Linz and died in 1859, while his mother came from the distinguished merchant family Pauernfeind of Salzburg. After graduating with honours at the academic gymnasium in Linz in 1863, he studied physics and mathematics at the University of Vienna. Among his university professors were: Jozef Maximilián →Petzval, Andreas von Ettingshausen, Johann Joseph Loschmidt, and Jožef →Stefan, who introduced him to the then very topical Maxwell electrodynamics and atomistics. B. already published two scientific works as a student. The second of these works dealt with his later life's work; the mechanical significance of the second law of the theory of heat. For this topic, he also received the support of Loschmidt. In 1867, a year after he completed his studies, he became an assistant under →Stefan at the Institute of Physics, and in 1868 a private assistant professor of mathematical physics. As soon as 1869, the 25-year-old B. became a full professor of mathematical physics at the University of Graz.

Unlike his teachers, B. tried to establish international scientific contacts. In the summer semester of 1870, he travelled to Robert Wilhelm Bunsen and Gustav Robert Kirchoff in Heidelberg, and in 1871/72 spent a few months working in the laboratory of Hermann Ludwig Ferdinand von Helmholtz in Berlin. There he began his experimental determination of the dielectric constant of insulators, which presented one of the first experimental confirmations of Maxwell's electromagnetic theory of light.

In 1872, B. formed a transport equation for the distribution of the density of gas molecules, deriving from Maxwell's statistical research. With this equation, he researched the transfer of gases from unbalanced states to a thermodynamic equilibrium. Today this equation is called Boltzmann equation. In this work, he formed his famous H-statement, in which H is the mean value of the logarithm of the distribution of the density of gas molecules in the so-called μ-space, which is stretched across three spatial coordinates and three velocity components into characteristic molecules. The value of H depends on the sign of the static analogy of the thermodynamic entropy S of a particular gas.

For this reason, B. at first named this value E, until this designation started being used in 1895 for denoting energy. The H-theorem states that with the distributional density of gas f(x, v, t) the function H = ∫ d3 x d3 v f(x, v, t) log f(x, v, t) is formed, under the statistical supposition that the velocities of individual gas molecules are at first uncorrelated (the hypothesis of molecular chaos), and that with the time t they increase or, at most, remain the same, when H reaches its minimum. This is completely analogous to the 2nd law of thermodynamics, which states that the entropy of a closed system increases until a thermodynamic equilibrium is attained. B. was thus able to mechanically explain the second law of thermodynamics, however, he at first applied it only to the balanced states of a defined notion of entropy, and later to unbalanced states as well. Unbalanced entropy defined in such a way is called »Boltzmann entropy«. Furthermore, B. was able to prove that the value of H for ideal gases in a thermodynamic equilibrium is directly proportional to the negative entropy of gases.

From 1873 to 1876, B. was a full professor of mathematics at the University of Vienna, but in 1876, he returned to Graz as a successor to A. Toeplers and as a director of the Physics Institute at the university. By objecting, his friend, Johann Joseph Loschmidt, encouraged him to generalise his statistical observations of the theory of heat, and concluded in 1877 that the entropy of a thermodynamic system of the value W can be realised and that via the macroscopic variables of pressure, temperature, volume etc. of the system's given macrostate, it is proportional to the numerous microstates; as noted by Max Planck S = k log W. This fundamental co-dependence, which became a basis for statistical mechanics, was named »Boltzmann's principle« by Albert Einstein in 1905. Since the value of the possibility of the realisation of a macrostate is proportional to its probability, this principle clearly explains the increase of entropy as a transition from highly unlikely unbalanced states to incomparable possibilities of balanced states.

In 1890, B. left Graz and taught theoretical physics in Munich, before returning to the University of Vienna in 1894 as →Stefan's successor. He stayed there, with the exception of a short intermission (from 1900 to 1902 in Leipzig), and in addition to teaching physics also lectured on the philosophy of nature between 1903 and 1906. Between 1895 and 1898, these lectures were held by Ernst →Mach. From these lectures, B. derived some of the most important views of the so-called evolutionary theory of cognition from the ontology of atomistics.

After the death of his mother in 1885, B. fell into a depression for the first time, which ended as late as 1888, when the German Emperor appointed him Kirchhoff's successor and he was forced to return to Berlin. He was also under the influence of this ailment in Leipzig.

Later on, periods of great mental activity interchanged with periods of severe depressions. The high stress he suffered as a consequence of his teaching activities and the strains of his third journey to America (1899, 1904 and 1905), aggravated his medical condition to the extent that he decided to commit suicide in 1906.

B. is one of the founders of statistical physics; his research paved the way for the turnaround in physics at the beginning of the 20th century. Planck's quantum hypothesis from 1900 was based on Boltzmann's works; B. even advised Planck slightly prior to that to use his statistical method. In 1905, the young Einstein published a theory of Brownian motion, which led to the quantitative determination of B.'s statistical oscillation. In addition to the above-mentioned works by B., his theory of elastic effect from 1876 deserves mention, as well as his ergodic hypothesis formulated in 1887, and his theoretical derivation of the »Stefan-Bolzmann law« from 1884. He applied the critical method to his scientific theory, and according to the statement by Ludwig Wittgenstein greatly influenced him.

Furthermore, as Karl Lorenz and Karl Popper maintained, he can be characterised as a predecessor of the evolutionary theory of cognition. His defence of atomism against positivism and phenomenalism could be classified as hypothetical realism.