Ludwig Eduard Boltzmann (/ˈbɒltsmən/,[1] US: /ˈboʊl-, ˈbɔːl-/;[1][2] German: [ˈluːtvɪk ˈbɔltsman]; 20 February 1844 – 5 September 1906) was an Austrian theoretical physicist and philosopher.

His grandfather, who had moved to Vienna from Berlin, was a clock manufacturer, and Boltzmann's mother, Katharina Pauernfeind, was originally from Salzburg.

[7] In 1869 at age 25, thanks to a letter of recommendation written by Josef Stefan,[8] Boltzmann was appointed full Professor of Mathematical Physics at the University of Graz in the province of Styria.

In 1869 he spent several months in Heidelberg working with Robert Bunsen and Leo Königsberger and in 1871 with Gustav Kirchhoff and Hermann von Helmholtz in Berlin.

In 1872, long before women were admitted to Austrian universities, he met Henriette von Aigentler, an aspiring teacher of mathematics and physics in Graz.

Ostwald offered Boltzmann the professorial chair in physics, which became vacant when Gustav Heinrich Wiedemann died.

[15] In 1905, he gave an invited course of lectures in the summer session at the University of California in Berkeley, which he described in a popular essay A German professor's trip to El Dorado.

[16] In May 1906, Boltzmann's deteriorating mental condition (described in a letter by the Dean as "a serious form of neurasthenia") forced him to resign his position.

[13] Boltzmann's kinetic theory of gases seemed to presuppose the reality of atoms and molecules, but almost all German philosophers and many scientists like Ernst Mach and the physical chemist Wilhelm Ostwald disbelieved their existence.

[23] In his work "On Thesis of Schopenhauer's", Boltzmann refers to his philosophy as materialism and says further: "Idealism asserts that only the ego exists, the various ideas, and seeks to explain matter from them.

Boltzmann was twenty-five years of age when he came upon James Clerk Maxwell's work on the kinetic theory of gases which hypothesized that temperature was caused by collision of molecules.

Maxwell used statistics to create a curve of molecular kinetic energy distribution from which Boltzmann clarified and developed the ideas of kinetic theory and entropy based upon statistical atomic theory creating the Maxwell–Boltzmann distribution as a description of molecular speeds in a gas.

Boltzmann also extended his theory in his 1877 paper beyond Carnot, Rudolf Clausius, James Clerk Maxwell and Lord Kelvin by demonstrating that entropy is contributed to by heat, spatial separation, and radiation.

To quote Planck, "The logarithmic connection between entropy and probability was first stated by L. Boltzmann in his kinetic theory of gases".

W (for Wahrscheinlichkeit, a German word meaning "probability") is the probability of occurrence of a macrostate[33] or, more precisely, the number of possible microstates corresponding to the macroscopic state of a system – the number of (unobservable) "ways" in the (observable) thermodynamic state of a system that can be realized by assigning different positions and momenta to the various molecules.

Boltzmann's paradigm was an ideal gas of N identical particles, of which Ni are in the ith microscopic condition (range) of position and momentum.

Also, the force acting on the particles depends directly on the velocity distribution function f. The Boltzmann equation is notoriously difficult to integrate.

Finally, in the 1970s E. G. D. Cohen and J. R. Dorfman proved that a systematic (power series) extension of the Boltzmann equation to high densities is mathematically impossible.

Following Maxwell,[36] Boltzmann modeled gas molecules as colliding billiard balls in a box, noting that with each collision nonequilibrium velocity distributions (groups of molecules moving at the same speed and in the same direction) would become increasingly disordered leading to a final state of macroscopic uniformity and maximum microscopic disorder or the state of maximum entropy (where the macroscopic uniformity corresponds to the obliteration of all field potentials or gradients).

[37] The second law, he argued, was thus simply the result of the fact that in a world of mechanically colliding particles disordered states are the most probable.

The gradual disordering of energy is analogous to the disordering of an initially ordered pack of cards under repeated shuffling, and just as the cards will finally return to their original order if shuffled a gigantic number of times, so the entire universe must some-day regain, by pure chance, the state from which it first set out.

(This optimistic coda to the idea of the dying universe becomes somewhat muted when one attempts to estimate the timeline which will probably elapse before it spontaneously occurs.

)[39] The tendency for entropy increase seems to cause difficulty to beginners in thermodynamics, but is easy to understand from the standpoint of the theory of probability.

For instance, Max Planck in quantizing resonators in his Black Body theory of radiation used the Boltzmann constant to describe the entropy of the system to arrive at his formula in 1900.

[41] However, Boltzmann's work was not always readily accepted during his lifetime, and he faced opposition from some of his contemporaries, particularly in regard to the existence of atoms and molecules.

Boltzmann's kinetic theory of gases was one of the first attempts to explain macroscopic properties, such as pressure and temperature, in terms of the behaviour of individual atoms and molecules.

Boltzmann's long-running dispute with the editor of a prominent German physics journal over the acceptance of atoms and molecules underscores the initial resistance to this idea.

Boltzmann's kinetic theory played a crucial role in demonstrating the reality of atoms and molecules and explaining various phenomena in gases, liquids, and solids.

Because the Boltzmann equation is practical in solving problems in rarefied or dilute gases, it has been used in many diverse areas of technology.

Thus, Boltzmann's early insights into the quantization of energy levels had a profound influence on the development of quantum physics.