# Ludwig Boltzmann

### Ludwig Boltzmann (1844–1906)

Austrian physicist who made pivotal contributions to thermodynamics and statistical mechanics, inventing several of the key notions of the latter field.The son of a taxation official, Boltzmann attended the University of Vienna and in 1866 earned a doctorate under the tutelage of Josef Stefan (1835–1893), whose empirical work on blackbody radiation Boltzmann would later put on a firm thermodynamic grounding. (Consequently, the statement that the total radiation from a blackbody goes as the fourth power of its temperature is today known as the Stefan–Boltzmann law.) After Stefan's death, Boltzmann took over his position as theoretical physics chair, but soon quit Vienna due to personal conflicts with the new chair of history and philosophy of science, Ernst Mach (1838–1916). He moved to Leipzig in 1900, where disputes over his theories led him to attempt suicide, unsuccessfully. Boltzmann returned to Vienna the following year, after Mach retired for health reasons, and in fact gained renown for his philosophy lectures — teaching the very class taught by Mach shortly before. In 1904, he traveled the United States, visiting the World's Fair in St. Louis; however, after his return to Europe, the attacks on his statistical mechanics work continued. Boltzmann committed suicide in Trieste, during a family vacation.

It is unknown whether Boltzmann's eventual suicide resulted from the scientific community's hostility to his work, a history of mental illness and melancholy, or some combination of both. (MacTutor biography)

Today, Boltzmann is renowned for having established a mathematical foundation of statistical physics, the study of large quantities of particles (such as atoms in a gas). To make calculations possible, Boltzmann devised the concept of an "ensemble", a set of many systems prepared in the same way. Thinking in terms of ensembles, one could calculate probabilities by working out what fraction of the ensemble's systems will exist in a given state. Each member of an ensemble satisfies the same macroscopic conditions; for example, they each have the same total energy. However, there are many different ways the atoms in a gas can move and still have the same total energy. Many *microstates* can be part of a single *macrostate.* The ensemble approach gave the first real understanding of what *entropy* means in statistical terms: the entropy of a macrostate is, up to a multiplicative factor, the logarithm of its number of microstates. (The multiplicative factor, known as Boltzmann's constant, sets the size of the degree marks on the temperature scale.)

Boltzmann also studied the way in which the entropy of a system rises with time. His mathematical deduction known as the *H*-theorem provided the first way to understand the Second Law of Thermodynamics in terms of individual atoms in motion.

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