Ludwig Boltzmann

Austrian physicist and philosopher (1844–1906)
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Ludwig Eduard Boltzmann (February 20, 1844September 5, 1906) was an Austrian physicist and philosopher famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. He was one of the most important advocates for atomic theory which was still highly controversial.

Ludwig Boltzmann (1902)


  • In my view all salvation for philosophy may be expected to come from Darwin's theory.
    • "Theoretical Physics and Philosophical Problems, Selected Writings", Ludwig Boltzmann, ed. B. McGuinness, 1974, p. 193
  • · ... Philosophy gets on my nerves. If we analyse the ultimate ground of everything, then everything finally falls into nothingness. But I have decided to resume my lectures again and look the Hydra of doubt straight in the eye, and it can be quite ominous [verhängnisvoll] if one values one's life. The title [Principles of Natural Philosophy] doesn't tell us anything coherent .... [it is] essentially a joke . . . . I must take care that the lecture is adequate. great difficulties; one doesn't really know what natural philosophy is ...
    • from Boltzmann's notes for his lecture on natural philosophy given on October 24, 1904, as quoted in Blackmore, J. T., ed. Ludwig Boltzmann His Later Life and Philosophy, 1900–1906: Book One: A Documentary History. Vol. 168. Springer Science & Business Media, 1995. p.136.
    • Itself quoting from Ilse M. Fasol-Boltzmann (ed.), Ludwig Boltzmann 'Principien der Naturfilosofi' - Lectures on Natural Philosophy 1903-1906, Springer-Verlag: Berlin etc., 1990. p. 107.
  • Let us now tum to the second matter in dispute between us [about the rejection of philosophy in virtually all senses]. That the majority of students don't understand philosophy doesn't bother me. But can any two people understand philosophical [i.e. metaphysical] questions [and agree upon what it is that they understand]? Is there any sense at all in breaking one's head over such questions? Shouldn't the irresistible pressure [Drang] to philosophize be compared with the nausea caused by migraine headaches? As if something could still struggle its strangled way out, even though nothing is actually there at all? My opinion about the high, majestic task of philosophy is to make things clear, in order to finally heal mankind from these terrible migraine headaches. Now, I am one who hopes not to make you angry by my forthrightness, but the first duty of philosophy as love of wisdom is complete frankness. Through my study of Schopenhauer, I am learning Greek ways of thinking again, but piecemeal.
    • letter to Franz Brentano (Vienna, January 4th, 1905), as quoted in Blackmore, J. T., ed. Ludwig Boltzmann His Later Life and Philosophy, 1900–1906: Book One: A Documentary History. Vol. 168. Springer Science & Business Media, 1995. p.125.
  • I take my stand before you as a reactionary, a survivor, who is still an enthusiast for the old and the classical as opposed to the modem.
    • a lecture at Munich in 1899. L. Boltzmann, Populare Schriften, Leipzig 1905, p. 205

Lectures on Gas Theory (1898)


Published in two volumes as Vorlesungen über Gastheorie. Translated by S.G. Brush, Lectures on Gas Theory, Berkeley: University of California Press, 1964.

  • I am conscious of being only an individual struggling weakly against the stream of time. But it still remains in my power to contribute in such a way that, when the theory of gases is again revived, not too much will have to be rediscovered. Thus in this book [this Part] I will now include the parts that are the most difficult and most subject to misunderstanding, and give (at least in outline) the most easily understood exposition of them.
    • Wie ohnmächtig der Einzelne gegen Zeitströmungen bleibt, ist mir bewusst. Um aber doch, was in meinen Kräften steht, dazu beizutragen, dass, wenn man wieder zur Gastheorie zurückgreift, nicht allzuviel noch einmal entdeckt werden muss, nahm ich in das vorliegende Buch nun auch die schwierigsten, dem Missverständnisse am meisten ausgesetzten Theile der Gastheorie auf und versuchte davon wenigstens in den Grundlinien eine möglichst leicht verständliche Darstellung zu geben.
    • Forward
  • Who sees the future? Let us have free scope for all directions of research; away with dogmatism, either atomistic or anti-atomistic!
    • p. 26

Translation of Ludwig Boltzmann’s Paper (2015)

"On the Relationship between the Second Fundamental Theorem of the Mechanical Theory of Heat and Probability Calculations Regarding the Conditions for Thermal Equilibrium" Sitzungberichte der Kaiserlichen Akademie der Wissenschaften. Mathematisch-Naturwissen Classe. Abt. II, LXXVI 1877, pp 373-435 (Wien. Ber. 1877, 76:373-435). Reprinted in Wiss. Abhandlungen, Vol. II, reprint 42, p. 164-223, Barth, Leipzig, (1909) Tr. Kim Sharp, Franz Matschinsky, Entropy 2015, 17(4), 1971-2009 An MDPI Open Access article. MDPI Open Access Information and Policy.
  • It is clear that every single uniform state distribution which establishes itself after a certain time given a defined initial state is equally as probable as every single nonuniform state distribution, comparable to the situation in the game of Lotto where every single quintet is as improbable as the quintet 12345. The higher probability that the state distribution becomes uniform with time arises only because there are far more uniform than nonuniform state distributions... It is even possible to calculate the probabilities from the relationships of the number of different state distributions. This approach would perhaps lead to an interesting method for the calculation of the equilibrium of heat.
    • from "Remarks about several problems of the mechanical theory of heat"
  • [I]t is possible to calculate the state of the equilibrium of heat by finding the probability of the different possible states of the system.
  • The initial state in most cases is bound to be highly improbable and from it the system will always rapidly approach a more probable state until it finally reaches the most probable state, i.e., that of the heat equilibrium.
  • [W]e will be able to identify that quantity which is usually called entropy with the probability of the particular state.
  • According to the second fundamental theorem... change has to take place in such a way that the total entropy of the particles increases. This means according to our present interpretation that nothing changes except that the probability of the overall state for all particles will get larger and larger.
  • The system of particles always changes from an improbable to a probable state.
  • [I]t is our main purpose not to limit our discussion to thermal equilibrium, but to explore the relationship of this probabilistic formulation to the second theorem of the mechanical theory of heat.
  • We want first to solve the problem... namely to calculate the probability of state distributions from the number of different distributions. We want first to treat as simple a case as possible, namely a gas of rigid absolutely elastic spherical molecules trapped in a container with absolutely elastic walls. Even in this case, the application of probability theory is not easy. The number of molecules is not infinite... yet the number of velocities each molecule is capable of is effectively infinite... to facilitate understanding, I will... consider a limiting case.
  • We assume initially, each molecule is only capable of assuming a finite number of velocities...
    where   and   are arbitrary finite numbers. ...but after the collision both molecules still have one of the above velocities ...the actual problem to be solved is re-established by letting p and q go to infinity.
  • [W]e will consider the kinetic energy, rather than the velocity of the molecules. Each molecule can have only a finite number of values for its kinetic energy. As a further simplification, we assume that the kinetic energies of each molecule form an arithmetic progression...
    We call   the largest possible value of the kinetic energy,  . ...after the collision, each molecule still has one of the above values of kinetic energy.


  • Eleganz sei die Sache der Schuster und Schneider
    • Elegance should be left to shoemakers and tailors
      • reported by Arnold Berliner, Curt Thesing (1946). Die Naturwissenschaften. Springer-Verlag. p. 36. 
      • also reported by Albert Einstein, translation by Robert W. Lawson (1921). Relativity. Plain Label Books. p. preface. ISBN 1-603-03164-2. 
  • O! immodest mortal! Your destiny is the joy of watching the evershifting battle!
  • Available energy is the main object at stake in the struggle for existence and the evolution of the world.
    • S. Rajasekar, N.Athavan, "Ludwig Edward Boltzmann"
  • Which is more remarkable fact about America: that millionaires are idealists or idealists become millionaires.
    • S. Rajasekar, N.Athavan, "Ludwig Edward Boltzmann"
  • Bring forward what is true, Write it so that it is clear, Defend it to your last breath!
    • S. Rajasekar, N.Athavan, "Ludwig Edward Boltzmann"
  • I am conscious of being only an individual struggling weakly against the stream of time. But it still remains in my power to contribute in such a way that, when the theory of gases is again revived, not too much will have to be rediscovered.
    • S. Rajasekar, N.Athavan, "Ludwig Edward Boltzmann"
  • The most ordinary things are to philosophy a source of insoluble puzzles. With infinite ingenuity it constructs a concept of space or time and then finds it absolutely impossible that there be objects in this space or that processes occur during this time.... the source of this kind of logic lies in excessive confidence in the so-called laws of thought.
    • S. Rajasekar, N.Athavan, "Ludwig Edward Boltzmann"

Quotes about Boltzmann

  • I adhered scrupulously to the precept of that brilliant theoretical physicist L. Boltzmann, according to whom matters of elegance ought to be left to the tailor and to the cobbler.
    • Albert Einstein, Preface to Relativity: The Special and the General Theory (1916)
  • Boltzmann’s Lectures on Gas Theory is an acknowledged masterpiece of theoretical physics... still... [of] considerable scientific value today. It contains a comprehensive exposition of the kinetic theory of gases by a scientist who devoted a large pail of his own career to it, and brought it very nearly to completion as a fundamental part of modern physics. ...Ludwig Boltzmann ...played a leading role in the nineteenth-century movement toward reducing the phenomena of heat, light, electricity, and magnetism to "matter and motion"—in other words, to atomic models based on Newtonian mechanics. His own greatest contribution was to show how... mechanics... previously ...regarded as deterministic and reversible in time, could be used to describe irreversible phenomena in the real world on a statistical basis. His original papers on the statistical interpretation of thermodynamics, the H-theorem, transport theory, thermal equilibrium, the equation of state of gases... occupy about 2,000 pages... [N]ot even the handful of experts on kinetic theory could claim to have read everything he wrote. ...Boltzmann decided to publish his lectures, in which the most important parts of the theory, including his ...contributions, were carefully explained. ...[H]e included his mature reflections and speculations on such questions as the nature of irreversibility and the justification for using statistical methods in physics. His Vorlesungen über Gastheorie was... the standard reference... for advanced researchers, ...[and] a popular textbook ...for the first quarter of the [20th] century ...
    • Stephen G. Brush, Translator's Introduction to Lectures on Gas Theory (1964) a translation of Ludwig Boltzmann's Vorlesungen iiber Gastheorie (1896, 1898)
  • The influence of Quetelet's ideas spread throughout the sciences, even to the physical sciences. The two primary founders of the modern kinetic theory of gases, based on considerations of probability, were James Clerk Maxwell and Ludwig Boltzmann. Both acknowledged their debt to Quetelet. ...historians generally consider the influence of the natural sciences on the social sciences, whereas in the case of Maxwell and Boltzmann, there is an influence of the social sciences on the natural sciences, as Theodore Porter has shown.
    • I. Bernard Cohen, The Triumph of Numbers: How Counting Shaped Modern Life (2005)
  • Boltzmann summarized most (but not all) of his work in a two volume treatise Vorlesungen Uber Gastheorie [1896, 1898]. This is one of the greatest books in the history of exact sciences and the reader is strongly advised to consult it. It is tough going but the rewards are great.
    • Mark Kac, Probability and Related Topics in Physical Sciences (1959) p. 261.
  • In 1902 he returned to his chair in theoretical physics... In addition to... mathematical physics, Boltzmann was given Mach's philosophy course to teach. His philosophy lectures quickly became famous with the audience... too large for the biggest lecture hall available. ...Boltzmann's fame is based on his invention of statistical mechanics... independently of Willard Gibbs. Their theories connected the properties and behaviour of atoms and molecules with... [those of] the substances of which they were the building blocks. ...Boltzmann obtained the Maxwell–Boltzmann distribution in 1871 ...In 1884 ...Boltzmann ...showed how Josef Stefan's empirical T4 law for black body radiation ...could be derived from the principles of thermodynamics. ...[T]he Second Law of Thermodynamics...he derived from the principles of mechanics in the 1890s.
  • In 1895, at a scientific meeting... Wilhelm Ostwald presented a paper... which... stated... The actual irreversibility of natural phenomena thus proves the existence of processes that cannot be described by mechanical equations, and with this the verdict on scientific materialism is settled.
    Sommerfeld... described the resulting battle between Ostwald and Boltzmann. ...Boltzmann was seconded by Felix Klein. The battle resembled the... bull with the supple fighter. However... the bull was victorious... Boltzmann carried the day. We, the young mathematicians of the time, were all on the side of Boltzmann...
    Boltzmann's ideas ...were opposed by many European scientists... not fully grasping the statistical nature of his reasoning.
  • Maxwell... during the 1860s... showed that when the [molecular] velocities reached the bell-shaped distribution, no further net change was likely. (...Ludwig Boltzmann further elaborated... and strengthened Maxwell's results). Any specific molecule would speed up or slow down, but... other molecules would change in speed to compensate. When a gas reached that state... the gas was at equilibrium. ...[T]his notion of equilibrium is precisely analogous to the Nash equilibrium in game theory. ...[J]ust as the Nash equilibrium is typically a mixed set of strategies, a gas seeks an equilibrium state with a mixed distribution of molecular velocities.
    • Tom Siegfried, A Beautiful Math (2006) Ch. 7: Quetelet's Statistics and Maxwell's Molecules, pp. 139-140.
  • Maxwell, and then Boltzmann, and then... J. Willard Gibbs consequently expended enormous intellectual effort in devising... statistical mechanics, or... statistical physics. The uses... extend far beyond gases... describing electric and magnetic interactions, chemical reactions, phase transitions... and all other manner of exchanges of matter and energy.
    The success... has driven the belief among many physicists that it could be applied with similar success to society. ...[E]verything from the flow of funds in the stock market to the flow of traffic on interstate highways ...
    • Tom Siegfried, A Beautiful Math (2006) Ch. 7: Quetelet's Statistics and Maxwell's Molecules, pp. 142-143.
  • Boltzmann... felt that all that we were really doing when we stated physical laws was using a series of linguistic representations of reality. To relate force and mass, as Newton had done in his laws of motion, was to relate labels in such a way that we could use the relations for predictive purposes. To read anything more into the terms force and mass was to presume more than we can know.
    • Brian L. Silver, The Ascent of Science (1998)

Ludwig Boltzmann: the Man who Trusted Atoms (1998)

by Carlo Cercignani
  • Boltzmann stands as a link between... James Clerk Maxwell... and Albert Einstein... Maxwell... first found the formula for the probability distribution of velocities of particles in a gas in equilibrium... but... Boltzmann... derived the equation governing the dynamical evolution of the probability distribution, according to which the state of a gas, not necessarily in equilibrium, will... change. Boltzmann's ideas were central to... Planck's... analysis of black body radiation... in which he introduced the quantum of action, thereby... the quantum revolution. In 1905 Einstein... developed it further (...showing that the "atomic hypothesis" applied even to light ..!) but was also influenced by Boltzmann's concepts in two... papers of 1905, one... a method of determining molecular dimensions and the other... explained... Brownian motion... Both gave enormous support to the "atomic hypothesis"...
    • Foreward
  • The Boltzmann equation was... the first... describing the time-evolution of a probability. ...[U]nlike ...equations governing the constituent particles ...[it] does not remain unchanged when ...time is reversed. The time-assymetry... arises as an aspect of the second law of thermodynamics... [i.e.,] the entropy of a system out of equilibrium increases with time. The crude meaning of... "entropy" is "disorder"; so... the order of a system is continually... reduced. ...Boltzmann ...give[s] precision to the... notion... identifying it with a... multiple of the logarithm of the volume in phase space defined by... macroscopic parameters specifying the state of the system. Accordingly... the second law could become amenable to precise mathematical treatment.
    • Foreward
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