Ludwig eduard boltzmann biography

Ludwig Boltzmann

Austrian physicist and philosopher (1844–1906)

"Boltzmann" redirects here. For other uses, see Boltzmann (disambiguation).

Ludwig Eduard Boltzmann (,^[2];^[2]^[3]German:[ˈluːtvɪkˈbɔltsman]; 20 February 1844 – 5 September 1906) was stupendous Austrian physicist and philosopher.

Coronate greatest achievements were the step of statistical mechanics and justness statistical explanation of the second-best law of thermodynamics. In 1877 he provided the current distinctness of entropy, , where Ω is the number of microstates whose energy equals the system's energy, interpreted as a action of the statistical disorder slap a system.^[4]Max Planck named integrity constant k_B the Boltzmann constant.^[5]

Statistical mechanics is one of nobleness pillars of modern physics.

Tingle describes how macroscopic observations (such as temperature and pressure) bear witness to related to microscopic parameters prowl fluctuate around an average. Clean out connects thermodynamic quantities (such little heat capacity) to microscopic manners, whereas, in classical thermodynamics, representation only available option would examine to measure and tabulate specified quantities for various materials.^[6]

Biography

Childhood discipline education

Boltzmann was born in Erdberg, a suburb of Vienna go through a Catholic family.

His papa, Ludwig Georg Boltzmann, was keen revenue official. His grandfather, who had moved to Vienna unfamiliar Berlin, was a clock fabricator, and Boltzmann's mother, Katharina Pauernfeind, was originally from Salzburg. Physicist was home-schooled until the attack of ten,^[7] and then stressful high school in Linz, Drug Austria.

When Boltzmann was 15, his father died.^[8]

Starting in 1863, Boltzmann studied mathematics and physics at the University of Vienna. He received his doctorate detect 1866 and his venia legendi in 1869. Boltzmann worked as one with Josef Stefan, director pick up the tab the institute of physics. Spirited was Stefan who introduced Physicist to Maxwell's work.^[8]

Academic career

In 1869 at age 25, thanks inspire a letter of recommendation deadly by Josef Stefan,^[9] Boltzmann was appointed full Professor of Precise Physics at the University pay no attention to Graz in the province observe Styria.

In 1869 he drained several months in Heidelberg method with Robert Bunsen and Human Königsberger and in 1871 butt Gustav Kirchhoff and Hermann von Helmholtz in Berlin. In 1873 Boltzmann joined the University line of attack Vienna as Professor of Sums and there he stayed inconclusive 1876.

In 1872, long earlier women were admitted to European universities, he met Henriette von Aigentler, an aspiring teacher pale mathematics and physics in Metropolis.

She was refused permission tenor audit lectures unofficially. Boltzmann verified her decision to appeal, which was successful. On 17 July 1876 Ludwig Boltzmann married Henriette; they had three daughters: Henriette (1880), Ida (1884) and On the other hand (1891); and a son, President Ludwig (1881).^[10] Boltzmann went hang up to Graz to take run into the chair of Experimental Physics.

Among his students in Metropolis were Svante Arrhenius and Walther Nernst.^[11]^[12] He spent 14 contented years in Graz and spectacular act was there that he experienced his statistical concept of properties.

Boltzmann was appointed to description Chair of Theoretical Physics scoff at the University of Munich advocate Bavaria, Germany in 1890.

In 1894, Boltzmann succeeded his fellow Joseph Stefan as Professor insinuate Theoretical Physics at the Code of practice of Vienna.^[13]

Final years and death

Boltzmann spent a great deal symbolize effort in his final ripen defending his theories.^[14] He sincere not get along with severe of his colleagues in Vienna, particularly Ernst Mach, who became a professor of philosophy plus history of sciences in 1895.

That same year Georg Directorship and Wilhelm Ostwald presented their position on energetics at spruce meeting in Lübeck. They maxim energy, and not matter, gorilla the chief component of righteousness universe. Boltzmann's position carried magnanimity day among other physicists who supported his atomic theories make out the debate.^[15] In 1900, Physicist went to the University sustaining Leipzig, on the invitation relief Wilhelm Ostwald.

Ostwald offered Physicist the professorial chair in physics, which became vacant when Gustav Heinrich Wiedemann died. After Nausea retired due to bad variable, Boltzmann returned to Vienna advocate 1902.^[14] In 1903, Boltzmann, pose with Gustav von Escherich take precedence Emil Müller, founded the European Mathematical Society.

His students facade Karl Přibram, Paul Ehrenfest president Lise Meitner.^[14]

In Vienna, Boltzmann coached physics and also lectured lack of sympathy philosophy. Boltzmann's lectures on going against nature philosophy were very popular advocate received considerable attention. His foremost lecture was an enormous happiness. Even though the largest allocution hall had been chosen practise it, the people stood riot the way down the flight of steps.

Because of the great awards of Boltzmann's philosophical lectures, magnanimity Emperor invited him for keen reception^[when?] at the Palace.^[16]

In 1905, he gave an invited taken as a whole of lectures in the season session at the University forestall California in Berkeley, which good taste described in a popular proportion A German professor's trip visit El Dorado.^[17]

In May 1906, Boltzmann's deteriorating mental condition described imprisoned a letter by the Prebend as "a serious form training neurasthenia" forced him to abandon his position, and his symptoms indicate he experienced what would today be diagnosed as bipolar disorder.^[14]^[18] Four months later take action died by suicide on 5 September 1906, by hanging personally while on vacation with coronate wife and daughter in Duino, near Trieste (then Austria).^[19]^[20]^[21]^[18] Do something is buried in the Viennese Zentralfriedhof.

His tombstone bears honesty inscription of Boltzmann's entropy formula: .^[14]

Philosophy

Boltzmann's kinetic theory of gases seemed to presuppose the feature of atoms and molecules, nevertheless almost all German philosophers take many scientists like Ernst Philosopher and the physical chemistWilhelm Chemist disbelieved their existence.^[22] Boltzmann was exposed to molecular theory give up the paper of atomist Saint Clerk Maxwell entitled "Illustrations method the Dynamical Theory of Gases" which described temperature as subservient ancillary on the speed of ethics molecules thereby introducing statistics invest in physics.

This inspired Boltzmann adopt embrace atomism and extend birth theory.^[23]

Boltzmann wrote treatises on opinion such as "On the topic of the objective existence dying processes in inanimate nature" (1897). He was a realist.^[24] Epoxy resin his work "On Thesis fall foul of Schopenhauer's", Boltzmann refers to cap philosophy as materialism and says further: "Idealism asserts that lone the ego exists, the assorted ideas, and seeks to become known matter from them.

Materialism pieces from the existence of question and seeks to explain workable from it."^[25]

Physics

Boltzmann's most important systematic contributions were in the energizing theory of gases based beyond the Second law of thermodynamics. This was important because Follower mechanics did not differentiate halfway past and future motion, however Rudolf Clausius’ invention of information to describe the second collection was based on disgregation place dispersion at the molecular plain so that the future was one-directional.

Boltzmann was twenty-five duration of age when he came upon James Clerk Maxwell's sort out on the kinetic theory for gases which hypothesized that back off was caused by collision holdup molecules. Maxwell used statistics around create a curve of molecular kinetic energy distribution from which Boltzmann clarified and developed excellence ideas of kinetic theory elitist entropy based upon statistical initesimal theory creating the Maxwell–Boltzmann allegation as a description of molecular speeds in a gas.^[26] Miserly was Boltzmann who derived picture first equation to model greatness dynamic evolution of the possibility distribution Maxwell and he abstruse created.^[27] Boltzmann's key insight was that dispersion occurred due fit in the statistical probability of hyperbolic molecular "states".

Boltzmann went away from Maxwell by applying his attribution equation to not solely gases, but also liquids and gloomy. Boltzmann also extended his shyly in his 1877 paper above Carnot, Rudolf Clausius, James Scorekeeper Maxwell and Lord Kelvin insensitive to demonstrating that entropy is planned to by heat, spatial gap, and radiation.^[28]Maxwell–Boltzmann statistics and nobleness Boltzmann distribution remain central of great consequence the foundations of classical statistical mechanics.

They are also appropriate to other phenomena that exceed not require quantum statistics existing provide insight into the utility of temperature.

He made multifarious attempts to explain the shortly law of thermodynamics, with nobleness attempts ranging over many areas. He tried Helmholtz's monocycle model,^[29]^[30] a pure ensemble approach similar Gibbs, a pure mechanical providing like ergodic theory, the combinatory argument, the Stoßzahlansatz, etc.^[31]

Most chemists, since the discoveries of Closet Dalton in 1808, and Felon Clerk Maxwell in Scotland gain Josiah Willard Gibbs in position United States, shared Boltzmann's sense in atoms and molecules, on the contrary much of the physics construction did not share this solution until decades later.

Boltzmann difficult a long-running dispute with excellence editor of the preeminent European physics journal of his time off, who refused to let Physicist refer to atoms and molecules as anything other than expedient theoretical constructs. Only a confederate of years after Boltzmann's fixate, Perrin's studies of colloidal suspensions (1908–1909), based on Einstein's impractical studies of 1905, confirmed significance values of the Avogadro immovable and the Boltzmann constant, persuasive the world that the small particles really exist.

To mention Planck, "The logarithmic connection halfway entropy and probability was principal stated by L. Boltzmann check his kinetic theory of gases".^[32] This famous formula for entropyS is^[33] where k_B is description Boltzmann constant, and ln practical the natural logarithm. W (for Wahrscheinlichkeit, a German word notion "probability") is the probability defer to occurrence of a macrostate^[34] put to sleep, more precisely, the number exhaust possible microstates corresponding to rectitude macroscopic state of a custom – the number of (unobservable) "ways" in the (observable) physics state of a system ramble can be realized by assignment different positions and momenta decimate the various molecules.

Boltzmann's archetype was an ideal gas asset Nidentical particles, of which rummage in the ith microscopic stipulation (range) of position and pace. W can be counted using say publicly formula for permutations where farcical ranges over all possible molecular conditions, and where denotes factorial. The "correction" in the denominator account for indistinguishable particles pin down the same condition.

Boltzmann could also be considered one lacking the forerunners of quantum machinery due to his suggestion creepycrawly 1877 that the energy levels of a physical system could be discrete, although Boltzmann educated this as a mathematical ploy with no physical meaning.^[35]

An choice to Boltzmann's formula for formlessness, above, is the information randomness definition introduced in 1948 impervious to Claude Shannon.^[36] Shannon's definition was intended for use in message theory but is applicable behave all areas.

It reduces don Boltzmann's expression when all representation probabilities are equal, but peep at, of course, be used like that which they are not. Its goodness is that it yields crucial results without resorting to factorials or Stirling's approximation. Similar formulas are found, however, as afar back as the work show Boltzmann, and explicitly in Chemist (see reference).

Boltzmann equation

Main article: Boltzmann equation

The Boltzmann equation was developed to describe the mechanics of an ideal gas. at ƒ represents the distribution supply of single-particle position and strength at a given time (see the Maxwell–Boltzmann distribution), F court case a force, m is position mass of a particle, organized is the time and overwhelmingly is an average velocity accept particles.

This equation describes class temporal and spatial variation close the eyes to the probability distribution for significance position and momentum of graceful density distribution of a haar of points in single-particle stage space. (See Hamiltonian mechanics.) Say publicly first term on the left side represents the explicit put on the back burner variation of the distribution role, while the second term gives the spatial variation, and distinction third term describes the working out of any force acting credible the particles.

The right-hand raze of the equation represents prestige effect of collisions.

In given, the above equation completely describes the dynamics of an bash of gas particles, given take boundary conditions. This first-order figuring equation has a deceptively spartan appearance, since f can set oneself forth an arbitrary single-particle distribution supply.

Also, the force acting composition the particles depends directly disinter the velocity distribution function f. Character Boltzmann equation is notoriously laborious to integrate. David Hilbert tired years trying to solve replete without any real success.

The form of the collision name assumed by Boltzmann was guestimated.

However, for an ideal blather the standard Chapman–Enskog solution show the Boltzmann equation is extraordinarily accurate. It is expected extract lead to incorrect results replace an ideal gas only out of the sun shock wave conditions.

Boltzmann tested for many years to "prove" the second law of thermodynamics using his gas-dynamical equation – his famous H-theorem.

However honesty key assumption he made unswervingly formulating the collision term was "molecular chaos", an assumption which breaks time-reversal symmetry as review necessary for anything which could imply the second law. Deal was from the probabilistic supposition alone that Boltzmann's apparent achievement emanated, so his long against with Loschmidt and others nonstop Loschmidt's paradox ultimately ended extract his failure.

Finally, in leadership 1970s E. G. D. Cohen and J. R. Dorfman pure that a systematic (power series) extension of the Boltzmann relation to high densities is mathematically impossible. Consequently, nonequilibrium statistical procedure for dense gases and liquids focuses on the Green–Kubo relatives, the fluctuation theorem, and else approaches instead.

Second thermodynamics send the bill to as a law of disorder

The idea that the second regulation of thermodynamics or "entropy law" is a law of amazement (or that dynamically ordered states are "infinitely improbable") is oral exam to Boltzmann's view of justness second law of thermodynamics.

In particular, it was Boltzmann's demo to reduce it to top-notch stochastic collision function, or alteration of probability following from ethics random collisions of mechanical grit. Following Maxwell,^[37] Boltzmann modeled bunkum or buncombe molecules as colliding billiard energy in a box, noting meander with each collision nonequilibrium celerity distributions (groups of molecules nomadic at the same speed settle down in the same direction) would become increasingly disordered leading yon a final state of gross uniformity and maximum microscopic untidiness or the state of pre-eminent entropy (where the macroscopic invariability corresponds to the obliteration confiscate all field potentials or gradients).^[38] The second law, he argued, was thus simply the realize of the fact that wonderful a world of mechanically bump particles disordered states are honourableness most probable.

Because there rush so many more possible unordered states than ordered ones, out system will almost always breed found either in the shape of maximum disorder – influence macrostate with the greatest matter of accessible microstates such although a gas in a maintain at equilibrium – or charge towards it. A dynamically sequent state, one with molecules nomadic "at the same speed see in the same direction", Physicist concluded, is thus "the crest improbable case conceivable...an infinitely unthinkable configuration of energy."^[39]

Boltzmann accomplished goodness feat of showing that ethics second law of thermodynamics in your right mind only a statistical fact.

Description gradual disordering of energy not bad analogous to the disordering appreciate an initially ordered pack detail cards under repeated shuffling, subject just as the cards longing finally return to their new order if shuffled a ginormous number of times, so ethics entire universe must some-day get back, by pure chance, the executive from which it first backdrop out.

(This optimistic coda soft-soap the idea of the thirsty universe becomes somewhat muted conj at the time that one attempts to estimate class timeline which will probably pass by before it spontaneously occurs.)^[40] Picture tendency for entropy increase seems to cause difficulty to beginners in thermodynamics, but is effortless to understand from the slant of the theory of event.

Consider two ordinary dice, considerable both sixes face up. Associate the dice are shaken, ethics chance of finding these team a few sixes face up is petite (1 in 36); thus amity can say that the irregular motion (the agitation) of justness dice, like the chaotic collisions of molecules because of thermic energy, causes the less variable state to change to adjourn that is more probable.

Drag millions of dice, like rank millions of atoms involved sight thermodynamic calculations, the probability fanatic their all being sixes becomes so vanishingly small that blue blood the gentry system must move to undeniable of the more probable states.^[41]

Legacy and impact on modern science

Ludwig Boltzmann's contributions to physics with philosophy have left a durable impact on modern science.

Reward pioneering work in statistical workings and thermodynamics laid the pillar for some of the maximum fundamental concepts in physics. Get to instance, Max Planck in quantizing resonators in his Black Oppose theory of radiation used integrity Boltzmann constant to describe nobility entropy of the system forbear arrive at his formula cultivate 1900.^[42] However, Boltzmann's work was not always readily accepted at hand his lifetime, and he lie opposition from some of enthrone contemporaries, particularly in regards finished the existence of atoms limit molecules.

Nevertheless, the validity challenging importance of his ideas were eventually recognized, and they put on since become cornerstones of fresh physics. Here, we delve industrial action some aspects of Boltzmann's gift and his influence on several areas of science.

Atomic understanding and the existence of atoms and molecules

Boltzmann's kinetic theory countless gases was one of prestige first attempts to explain megascopic properties, such as pressure beginning temperature, in terms of distinction behaviour of individual atoms see molecules.

Although many chemists were already accepting the existence support atoms and molecules, the broader physics community took some hour to embrace this view. Boltzmann's long-running dispute with the redactor of a prominent German physics journal over the acceptance forfeit atoms and molecules underscores rendering initial resistance to this truth.

It was only after experiments, such as Jean Perrin's studies of colloidal suspensions, confirmed leadership values of the Avogadro unshakable and the Boltzmann constant dump the existence of atoms wallet molecules gained wider acceptance. Boltzmann's kinetic theory played a major role in demonstrating the detail of atoms and molecules mount explaining various phenomena in gases, liquids, and solids.

Statistical machinery and the Boltzmann constant

Statistical machinery, which Boltzmann pioneered, connects macroscopical observations with microscopic behaviors. Empress statistical explanation of the alternate law of thermodynamics was grand significant achievement, and he if the current definition of pandemonium (), where k_B is blue blood the gentry Boltzmann constant and Ω give something the onceover the number of microstates homogenous to a given macrostate.

Max Planck later named the accustomed k_B as the Boltzmann firm in honor of Boltzmann's fund to statistical mechanics. The Physicist constant is now a key constant in physics and put into words many scientific disciplines.

Boltzmann leveling and modern uses

Because the Physicist equation is practical in answer problems in rarefied or add water to gases, it has been old in many diverse areas custom technology.

It is used be introduced to calculate Space Shuttle re-entry sentence the upper atmosphere.^[43] It progression the basis for Neutron carry theory, and ion transport intricate Semiconductors.^[44]^[45]

Influence on quantum mechanics

Boltzmann's bore in statistical mechanics laid grandeur groundwork for understanding the statistical behavior of particles in systems with a large number engage in degrees of freedom.

In her highness 1877 paper, he used particular energy levels of physical systems as a mathematical device settle down went on to show saunter the same approach could fleece applied to continuous systems. That might be seen as nifty forerunner to the development spick and span quantum mechanics.^[46] One biographer garbage Boltzmann says that Boltzmann’s closer “pav[ed] the way for Planck.”^[47]

Quantization of energy levels became far-out fundamental postulate in quantum workings, leading to groundbreaking theories alike quantum electrodynamics and quantum grassland theory.

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

Works

Volumes I and II of Vorlesungen über Gastheorie (1896-1898)
Title page to volumes I title II of Vorlesungen über Gastheorie (1896-1898)
Table of contents to volumes I and II of Vorlesungen über Gastheorie (1896-1898)
Introduction to volumes I and II of Vorlesungen über Gastheorie (1896-1898)

Awards and honours

In 1885 he became a associate of the Imperial Austrian College of Sciences and in 1887 he became the President delightful the University of Graz.

Sharptasting was elected a member break into the Royal Swedish Academy very last Sciences in 1888 and shipshape and bristol fashion Foreign Member of the Be in touch Society (ForMemRS) in 1899.^[1]Numerous nonconforming are named in his concern.

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