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Encyclopedia > Ludwig Boltzmann

Ludwig Eduard Boltzmann (Vienna, Austrian Empire, February 20, 1844Duino near Trieste, September 5, 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. Vienna (German: Wien ) is the capital of Austria, and also one of the nine States of Austria. ... Flag of the Habsburg Monarchy The Crown of the Austrian Emperor For the history of these states before 1804, see Holy Roman Empire, Habsburg Monarchy, and articles on each of the component countries. ... February 20 is the 51st day of the year in the Gregorian Calendar. ... 1844 was a leap year starting on Monday (see link for calendar). ... Duino castle Duino (Devin in Slovenian, Tybein in German) in the coastal part of the Municipality of Duino-Aurisina, lies in the region of Friuli-Venezia Giulia in the province of Trieste, in north-east Italy. ... Country Italy Region Friuli-Venezia Giulia Province Trieste (TS) Mayor Roberto Dipiazza (since 2001) Elevation 2 m Area 8,449 kmÂ² Population  - Total (as of December 31, 2004) 207,069  - Density 2,480/kmÂ² Time zone CET, UTC+1 Coordinates Gentilic Triestini Dialing code 040 Postal code 34100 Frazioni See... September 5 is the 248th day of the year (249th in leap years). ... 1906 (MCMVI) was a common year starting on Monday (see link for calendar). ... Physicists working in a government lab A physicist is a scientist who is a practitioner of physics. ... Statistical mechanics is the application of statistics, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... Statistical mechanics is the application of statistics, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ...

Ludwig Boltzmann

Image File history File links Boltzmann2. ... Image File history File links Boltzmann2. ...

## Childhood and Education

Ludwig Edward Boltzmann was born on February 20, 1844 in Vienna. His father, Ludwig Georg Boltzmann was a tax official. His grandfather, who had moved to Vienna from Berlin, was a clock manufacturer, and Boltzmann’s mother, Katharina Pauernfeind, was originally from Salzburg. He received his primary education from a private tutor at the home of his parents. Boltzmann attended high school in Linz, Upper Austria. At age 15, Boltzmann lost his father. February 20 is the 51st day of the year in the Gregorian Calendar. ... 1844 was a leap year starting on Monday (see link for calendar). ... Vienna (German: Wien ) is the capital of Austria, and also one of the nine States of Austria. ... Berlin is the capital city and a state of Germany. ... Flag of Salzburg Salzburg (population 145,000 in 2005) is a city in western Austria and the capital of the federal state of Salzburg (population 520,000 in 2003). ... Map of Austria, locating Linz Linz is a city and Statutarstadt in northeast Austria, on the Danube river. ... Upper Austria (Ober sterreich) is one of the nine federal states or Bundesl nder of Austria. ...

Boltzmann studied physics at the University of Vienna, starting in 1863. Among his teachers were Josef Loschmidt, Joseph Stefan, Andreas von Ettingshausen and Jozef Petzval. Boltzmann received his PhD degree in 1866 working under the supervision of Stefan; his dissertation was on kinetic theory of gases. In 1867 he became a Privatdozent (lecturer). After obtaining his doctorate degree, Boltzmann worked two more years as Stefan’s assistant. It was Stefan who introduced Boltzmann to Maxwell's work. The first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density. ... Please wikify (format) this article or section as suggested in the Guide to layout and the Manual of Style. ... Johann Josef Loschmidt (March 15, 1821 - July 8, 1895) was an Austrian physicist and chemist. ... Joseph Stefan (Slovene JoÅ¾ef Stefan) (March 24, 1835 â€“ January 7, 1893) was a Slovene physicist, mathematician and poet. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... 1866 (MDCCCLXVI) is a common year starting on Monday of the Gregorian calendar or a common year starting on Wednesday of the 12-day-slower Julian calendar. ... Privatdozent (PD or Priv. ... James Clerk Maxwell (13 June 1831 â€“ 5 November 1879) was a Scottish mathematical physicist, born in Edinburgh. ...

In 1869, at age 25, he 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 then in 1871 he was with Gustav Kirchhoff and Hermann von Helmholtz in Berlin. In 1873 Boltzmann joined the University of Vienna as Professor of Mathematics and where he stayed till 1876. 1869 (MDCCCLXIX) is a common year starting on Friday (link will take you to calendar) of the Gregorian calendar or a common year starting on Sunday of the 12-day-slower Julian calendar. ... The University of Graz (founded 1585), a university located in Graz, Austria, is the second-largest university in Austria. ... Styria (Steiermark in German, Štajerska in Slovenian) can refer to: Styria - a federal state of Austria Styria - an informal province in Slovenia Styria - a duchy of the Holy Roman Empire and crownland of Austria-Hungary This is a disambiguation page — a navigational aid which lists other pages that might otherwise... 1869 (MDCCCLXIX) is a common year starting on Friday (link will take you to calendar) of the Gregorian calendar or a common year starting on Sunday of the 12-day-slower Julian calendar. ... Heidelberg is a scenic city in Baden-WÃ¼rttemberg, Germany, halfway between Stuttgart and Frankfurt. ... Robert Bunsen Robert Wilhelm Bunsen (31 March 1811 â€“ 16 August 1899) was a German chemist. ... Photograph of Leo KÃ¶nigsberger, 1886 Leo KÃ¶nigsberger (October 15, 1837â€“December 15, 1921) was a German mathematician, and historian of science. ... Gustav Kirchhoff Gustav Robert Kirchhoff (March 12, 1824 â€“ October 17, 1887), a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. ... Hermann von Helmholtz Hermann Ludwig Ferdinand von Helmholtz (August 31, 1821 â€“ September 8, 1894) was a German physician and physicist. ... 1873 (MDCCCLXXIII) was a common year starting on Wednesday (see link for calendar). ... Please wikify (format) this article or section as suggested in the Guide to layout and the Manual of Style. ... 1876 (MDCCCLXXVI) was a leap year starting on Saturday. ...

Ludwig Boltzmann and co-workers in Graz, 1887. (standing, from the left) Nernst, Streintz, Arrhenius, Hiecke, (sitting, from the left) Aulinger, Ettingshausen, Boltzmann, Klemenčič, Hausmanninger

In 1872, long before women were admitted to Austrian universities, he met Henriette von Aigentler, an aspiring teacher of mathematics and physics in Graz. She was refused permission to unofficially audit lectures, and Boltzmann advised her to appeal; she did, successfully. On July 17, 1876 Ludwig Boltzmann married Henriette von Aigentler; they had three daughters and two sons. Boltzmann went back to Graz to take up the chair of Experimental Physics. Among his students in Graz were Svante Arrhenius, and Walther Nernst. He spent 14 happy years in Graz and it was there that he developed his statistical concept of nature. In 1885 he became member of the Imperial Austrian Academy of Sciences and in 1887 he became the President of the University of Graz. Image File history File links Boltzmann-grp. ... Image File history File links Boltzmann-grp. ... Walther Nernst. ... Svante August Arrhenius Svante August Arrhenius (February 19, 1859 â€“ October 2, 1927) was a Swedish chemist and one of the founders of the science of physical chemistry. ... Ignacij KlemenÄiÄ (February 6, 1853 - September 5, 1901) was a Slovene physicist. ... July 17 is the 198th day (199th in leap years) of the year in the Gregorian calendar, with 167 days remaining. ... Svante August Arrhenius Svante August Arrhenius (February 19, 1859 â€“ October 2, 1927) was a Swedish chemist and one of the founders of the science of physical chemistry. ... Walther Nernst. ... 1885 (MDCCCLXXXV) is a common year starting on Thursday. ... 1887 (MDCCCLXXXVII) is a common year starting on Saturday (click on link for calendar) of the Gregorian calendar or a common year starting on Monday of the Julian calendar. ... The University of Graz (founded 1585), a university located in Graz, Austria, is the second-largest university in Austria. ...

Boltzmann was appointed to the Chair of Theoretical Physics at the University of Munich in Bavaria, Germany in 1890. In 1893, Boltzmann succeeded his teacher Joseph Stefan as Professor of Theoretical Physics at the University of Vienna. However, Boltzmann did not get along with some of his colleagues there; particularly when Ernst Mach became professor of philosophy and history of sciences in 1895. Thus in 1900 Boltzmann went to the University of Leipzig, on the invitation of Wilhelm Ostwald. After the retirement of Mach due to bad health, Boltzmann came back to Vienna in 1902, where he stayed until his death. Among his students there were Karl Przibram, Paul Ehrenfest and Lise Meitner. With approximately 48,000 students, the Ludwig-Maximilians-University Munich (German: Ludwig-Maximilians-Universität München or LMU) is one of the largest universities in Germany. ... The Free State of Bavaria  (German: Freistaat Bayern), with an area of 70,553 kmÂ² (27,241 square miles) and 12. ... 1890 (MDCCCXC) was a common year starting on Wednesday (see link for calendar) of the Gregorian calendar (or a common year starting on Friday of the Julian calendar). ... Ernst Mach Ernst Mach (February 18, 1838 â€“ February 19, 1916) was an Austrian-Czech physicist and philosopher and is the namesake for the Mach number and the optical illusion known as Mach bands. ... 1900 (MCM) was an exceptional common year starting on Monday. ... The University of Leipzig (UniversitÃ¤t Leipzig), located in Leipzig in the Free State and former Kingdom of Saxony, is one of the oldest universities in Europe. ... Wilhelm Ostwald Friedrich Wilhelm Ostwald (commonly just Wilhelm Ostwald) (September 2, 1853 - April 4, 1932) was a German chemist. ... 1902 (MCMII) was a common year starting on Wednesday (see link for calendar). ... Paul Ehrenfest Paul Ehrenfest (Vienna, January 18, 1880 â€“ Amsterdam, September 25, 1933) was an Austrian physicist and mathematician, who obtained Dutch citizenship on March 24, 1922. ... Lise Meitner ca. ...

In Vienna, Boltzmann not only taught physics but also lectured on philosophy. Boltzmann’s lectures on natural philosophy were very popular, and received a considerable attention at that time. His first lecture was an enormous success. Even though the largest lecture hall had been chosen for it, the people stood all the way down the staircase. Because of the great successes of Boltzmann’s philosophical lectures, the Emperor invited him for a reception at the Palace.

## Overview

Much of the physics establishment rejected his thesis about the reality of atoms and molecules — a belief shared, however, by Maxwell in Scotland and Gibbs in the United States; and by most chemists since the discoveries of John Dalton in 1808. He had a long-running dispute with the editor of the preeminent German physics journal of his day, who refused to let Boltzmann refer to atoms and molecules as anything other than convenient theoretical constructs. Only a couple of years after Boltzmann's death, Perrin's studies of colloidal suspensions (1908-1909) confirmed the values of Avogadro's number and Boltzmann's constant, and convinced the world that the tiny particles really exist. The first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density. ... Properties For other uses, see Atom (disambiguation). ... In chemistry, a molecule is an aggregate of at least two atoms in a definite arrangement held together by special forces. ... James Clerk Maxwell (13 June 1831 â€“ 5 November 1879) was a Scottish mathematical physicist, born in Edinburgh. ... Motto: (Latin for No one provokes me with impunity)1 Anthem: Multiple unofficial anthems Capital Edinburgh Largest city Glasgow Official language(s) English, Gaelic, Scots2 Government Constitutional monarchy  - Queen Queen Elizabeth II  - Prime Minister Tony Blair MP  - First Minister Jack McConnell MSP Unification    - by Kenneth I 843  Area    - Total 78... Josiah Willard Gibbs (February 11, 1839 â€“ April 28, 1903) was an American mathematical physicist who contributed much of the theoretical foundation for chemical thermodynamics. ... Portrait of Monsieur Lavoisier and his Wife, by Jacques-Louis David The history of chemistry may be said to begin with the distinction of chemistry from alchemy by Robert Boyle in his work The Skeptical Chymist, which was written after a long and tearfilled talk with his father, and alchymist... Chemistry (from the Greek word Ï‡Î·Î¼ÎµÎ¯Î± (chemeia) meaning cast together or pour together) is the science of matter at the atomic to molecular scale, dealing primarily with collections of atoms (such as molecules, crystals, and metals). ... John Dalton John Dalton (September 6, 1766 â€“ July 27, 1844) was a British chemist and physicist, born at Eaglesfield, near Cockermouth in Cumberland. ... The word theory has a number of distinct meanings in different fields of knowledge, depending on the context and their methodologies. ... Jean Baptiste Perrin (b. ... In general, a colloid or colloidal dispersion is a substance with components of one or two phases, a type of mixture intermediate between homogeneous solution and heterogeneous mixture with properties also intermediate between a solution and a mixture. ... Avogadros number, also called Avogadros constant (NA) is a large constant used in chemistry and physics. ... Ludwig Boltzmann The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ... In physics, atomic theory is a theory of the nature of matter. ...

To quote Planck, The logarithmic connection between entropy and probability was first stated by L. Boltzmann in his kinetic theory of gases.[1] This famous formula for entropy S is[2] [3] Max Planck Max Karl Ernst Ludwig Planck (April 23, 1858 â€“ October 4, 1947) was one of the most important German physicists of the late 19th and early 20th century; he is considered to be the founder of quantum theory. ... Logarithms to various bases: is to base e, is to base 10, and is to base 1. ... In thermodynamics, entropy, symbolized by S, is a state function of a thermodynamic system defined by the differential quantity , where dQ is the amount of heat absorbed in a reversible process in which the system goes from the one state to another, and T is the absolute temperature. ... This article is about probability. ... Kinetic theory attempts to explain macroscopic properties of gases, such as pressure, temperature, or volume, by considering their molecular composition and motion. ...

$S = k , log W$

where k = 1.3806505(24) × 10−23 J K−1 is Boltzmann's constant, and the logarithm is taken to the natural base e. W is the number of possible microstates corresponding to the macroscopic state of a system — the number of (unobservable) "ways" the (observable) thermodynamic state of a system 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 i-th microscopic condition (range) of position and momentum. W can be counted using the formula for permutations The joule (symbol: J) is the SI unit of energy, or work with base units of kgÂ·mÂ²/sÂ² (NÂ·m). ... The kelvin (symbol: K) is the SI unit of temperature, and is one of the seven SI base units. ... Ludwig Boltzmann The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ... Logarithms to various bases: is to base e, is to base 10, and is to base 1. ... In statistical mechanics, a microstate describes a specific detailed microscopic configuration of a system, that the system visits in the course of its thermal fluctuations. ... Macroscopic is commonly used to describe physical objects that are measurable and observable by the naked eye. ... â€¹ The template below has been proposed for deletion. ... In mathematics as applied to geometry, physics or engineering, a coordinate system is a system for assigning a tuple of numbers to each point in an n-dimensional space. ... In classical mechanics, momentum (pl. ... Since the late 1960s, the word paradigm (IPA: ) has referred to a thought pattern in any scientific discipline or other epistemological context. ... An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of negligible volume, with no intermolecular forces. ... It has been suggested that the section Physical applications of the Maxwell-Boltzmann distribution from the article Maxwell-Boltzmann distribution be merged into this article or section. ...

$W = N!; / ; prod_i N_i!$

where i ranges over all possible molecular conditions. (! denotes factorial.) The "correction" in the denominator is due to the fact that identical particles in the same condition are indistinguishable. W is called the "thermodynamic probability" since it is an integer greater than one, while mathematical probabilities are always numbers between zero and one. In mathematics, the factorial of a natural number n is the product of all positive integers less than or equal to n. ... Identical particles, or indistinguishable particles, are particles that cannot be distinguished from one another, even in principle. ... The integers consist of the positive natural numbers (1, 2, 3, â€¦), their negatives (âˆ’1, âˆ’2, âˆ’3, ...) and the number zero. ... Probability theory is the mathematical study of probability. ... A number is an abstract entity that represents a count or measurement. ...

The equation for S is engraved on Boltzmann's tombstone at the Vienna Zentralfriedhof — his second grave. Headstones in the Japanese Cemetry in Broome, Western Australia A cemetery in rural Spain A typical late 20th century headstone in the United States A headstone, tombstone or gravestone is a marker, normally carved from stone, placed over or next to the site of a burial. ... Exterior of the Dr. Karl Lueger-GedÃ¤chtniskirche, Zentralfriedhof, Vienna. ...

## The Boltzmann equation

Boltzmann's bust in the courtyard arcade of the main building, University of Vienna.
Main article: Boltzmann equation

The Boltzmann equation was developed to describe the dynamics of an ideal gas. Download high resolution version (2560x1920, 990 KB) Bust of Ludwig Boltzmann, physicist, in the courtyard arcade of the main building, University of Vienna, Austria. ... Download high resolution version (2560x1920, 990 KB) Bust of Ludwig Boltzmann, physicist, in the courtyard arcade of the main building, University of Vienna, Austria. ... Please wikify (format) this article or section as suggested in the Guide to layout and the Manual of Style. ... The Boltzmann equation describes the statistical distribution of particles in a fluid. ... An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of negligible volume, with no intermolecular forces. ...

$frac{partial f}{partial t}+ v frac{partial f}{partial x}+ frac{F}{m} frac{partial f}{partial v} = frac{partial f}{partial t}left.{!!frac{}{}}right|_mathrm{collision}$

where f represents the distribution function of single-particle position and momentum at a given time (see the Maxwell-Boltzmann distribution), F is a force, m is the mass of a particle, t is the time and v is an average velocity of particles. The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ...

This equation describes the temporal and spatial variation of the probability distribution for the position and momentum of a density distribution of a cloud of points in single-particle phase space. (See Hamiltonian mechanics.) The first term on the left-hand side represents the explicit time variation of the distribution function, while the second term gives the spatial variation, and the third term describes the effect of any force acting on the particles. The right-hand side of the equation represents the effect of collisions. A pocket watch, a device used to measure time. ... Space has been an interest for philosophers and scientists for much of human history, and hence it is difficult to provide an uncontroversial and clear definition outside of specific defined contexts. ... Phase space of a dynamical system with focal stability. ... Hamiltonian mechanics is a re-formulation of classical mechanics that was invented in 1833 by William Rowan Hamilton. ...

Boltzmann's grave in the Zentralfriedhof, Vienna, with bust and entropy formula.

In principle, the above equation completely describes the dynamics of an ensemble of gas particles, given appropriate boundary conditions. This first-order differential equation has a deceptively simple appearance, since f can represent an arbitrary single-particle distribution function. Also, the force acting on the particles depends directly on the velocity distribution function f. The Boltzmann equation is notoriously difficult to integrate. David Hilbert spent years trying to solve it without any real success. Download high resolution version (1920x2560, 973 KB) Grave of Ludwig Boltzmann, physicist, Zentralfriedhof (Central Cemetery), Vienna, Austria. ... Download high resolution version (1920x2560, 973 KB) Grave of Ludwig Boltzmann, physicist, Zentralfriedhof (Central Cemetery), Vienna, Austria. ... Exterior of the Dr. Karl Lueger-GedÃ¤chtniskirche, Zentralfriedhof, Vienna. ... In mathematics, boundary conditions are imposed on the solutions of ordinary differential equations and partial differential equations, to fit the solutions to the actual problem. ... Graph of a differential equation In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ... In physics, force is that which changes or tend to change the state of rest or motion of a body. ... In calculus, the integral of a function is a generalization of area, mass, volume and total. ... David Hilbert (January 23, 1862, Wehlau, East Prussia â€“ February 14, 1943, GÃ¶ttingen, Germany) was a German mathematician, recognized as one of the most influential mathematicians of the 19th and early 20th centuries. ...

The form of the collision term assumed by Boltzmann was approximate. However for an ideal gas the standard Chapman-Enskog solution of the Boltzmann equation is highly accurate. It is only expected to lead to incorrect results for an ideal gas under shock-wave conditions. An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of negligible volume, with no intermolecular forces. ... An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of negligible volume, with no intermolecular forces. ...

Boltzmann tried for many years to "prove" the second law of thermodynamics using his gas-dynamical equation — his famous H-theorem.[4] However the key assumption he made in formulating the collision term was "molecular chaos", an assumption which breaks time-reversal symmetry as is necessary for anything which could imply the second law. It was from the probabilistic assumption alone that Boltzmann's apparent success emanated, so his long dispute with Loschmidt and others over Loschmidt's paradox ultimately ended in his failure. The second law of thermodynamics states that which is equivalent to this scientific statement: The Second Law is a statistical law and thus applicable only to macroscopic systems. ... In thermodynamics, the H-theorem describes the increase of entropy of an ideal gas in an irreversible process, solving the Boltzmann equation. ... In kinetic theory in physics, molecular chaos is the assumption that the velocities of colliding particles are uncorrelated, and independent of position. ... CPT-symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity and time simultaneously. ... Johann Josef Loschmidt (March 15, 1821 - July 8, 1895) was an Austrian physicist and chemist. ... Loschmidts paradox states that if there is a motion of a system that leads to a steady decrease of H (increase of entropy) with time, then there is certainly another allowed state of motion of the system, found by time reversal, in which H must increase. ...

For higher density fluids, the Enskog equation was proposed. For moderately dense gases this equation, which reduces to the Boltzmann equation at low densities, is fairly accurate. However the Enskog equation is basically an heuristic approximation without any rigorous mathematical basis for extrapolating from low to higher densities. Heuristic is the art and science of discovery and invention. ... It has been suggested that this article or section be merged with estimation. ... In mathematics, extrapolation is a type of interpolation. ...

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. Consequently nonequilibrium statistical mechanics for dense gases and liquids focuses on the Green-Kubo relations, the fluctuation theorem, and other approaches instead. A gas is one of the four main phases of matter (after solid and liquid, and followed by plasma), that subsequently appear as a solid material is subjected to increasingly higher temperatures. ... A liquid will assume the shape of its container. ... Green-Kubo relations give exact mathematical expression for transport coefficients in terms of integrals of time correlation functions. ... The second law of thermodynamics stands in apparent contradiction with the time reversible equations of motion for classical and quantum systems. ...

## Energetics of evolution

In 1922, Alfred J. Lotka [5] referred to Boltzmann as one of the first proponents of the proposition that available energy (also called exergy) can be understood as the fundamental object under contention in the biological, or life-struggle and therefore also in the evolution of the organic world. Lotka interpreted Boltzmann's view to imply that available energy could be the central concept that unified physics and biology as a quantitative physical principle of evolution. Howard T. Odum later developed this view as the maximum power principle. Energetics is the scientific study of energy flows under transfomation. ... Alfred James Lotka (March 2, 1880 - December 5, 1949) was a US mathematician and statistician, most famous for his work in population dynamics. ... This article needs to be cleaned up to conform to a higher standard of quality. ... Howard Thomas Odum (1924-2002), commonly known as H.T. Odum or Tom Odum, was an eminent American ecosystem ecologist and a professor at the University of Florida. ... This article or section may be confusing for some readers, and should be edited to be clearer. ...

## Significant contributions

1872 - Boltzmann equation; H-theorem 1872 (MDCCCLXXII) was a leap year starting on Monday (see link for calendar) of the Gregorian calendar or a leap year starting on Wednesday of the 12-day-slower Julian calendar. ... The Boltzmann equation describes the statistical distribution of particles in a fluid. ... In thermodynamics, the H-theorem describes the increase of entropy of an ideal gas in an irreversible process, solving the Boltzmann equation. ...

1877 - Boltzmann distribution; relationship between thermodynamic entropy and probability. 1877 (MDCCCLXXVII) was a common year starting on Monday (see link for calendar). ... The Maxwell-Boltzmann distribution is a probability distribution with applications in physics and chemistry. ...

1884 - Derivation of the Stefan-Boltzmann law 1884 (MDCCCLXXXIV) is a leap year starting on Tuesday (click on link to calendar) of the Gregorian calendar (or a leap year starting on Thursday of the 12-day-slower Julian calendar). ... Stefan-Boltzmann law (also Stefans law) states that tom is a brain the total energy radiated per unit surface area of a black body in unit time (black-body irradiance), (or the energy flux density (radiant flux) or the emissive power), j* is directly proportional to the fourth power...

## Evaluations

Closely associated with a particular interpretation of the second law of thermodynamics, he is also credited in some quarters with anticipating quantum mechanics. The second law of thermodynamics states that which is equivalent to this scientific statement: The Second Law is a statistical law and thus applicable only to macroscopic systems. ... Fig. ...

For detailed and technically informed account of Boltzmann's contributions to statistical mechanics consult the article by E.G.D. Cohen.

See also: Philosophy of thermal and statistical physics. The philosophy of thermal and statistical physics is one of the major subdisciplines of the philosophy of physics. ...

## Final years

Boltzmann was subject to rapid alternation of depressed moods with elevated, expansive or irritable moods. He himself jestingly attributed his rapid swings in temperament to the fact that he was born during the night between Mardi Gras and Ash Wednesday; he was, almost certainly, manic-depressive. Meitner relates that those who were close to Boltzmann were aware of his bouts of severe depression and his suicide attempts. Tragically, on September 5, 1906, while on a summer vacation in Duino near Trieste he committed suicide during an attack of depression. Bipolar disorder (previously known as manic depression) is a diagnostic category describing a class of mood disorders in which the person experiences states or episodes of depression and/or mania, hypomania, and/or mixed states. ... Duino castle Duino (Devin in Slovenian, Tybein in German) in the coastal part of the Municipality of Duino-Aurisina, lies in the region of Friuli-Venezia Giulia in the province of Trieste, in north-east Italy. ... Country Italy Region Friuli-Venezia Giulia Province Trieste (TS) Mayor Roberto Dipiazza (since 2001) Elevation 2 m Area 8,449 kmÂ² Population  - Total (as of December 31, 2004) 207,069  - Density 2,480/kmÂ² Time zone CET, UTC+1 Coordinates Gentilic Triestini Dialing code 040 Postal code 34100 Frazioni See... Suicide (from Latin sui caedere, to kill oneself) is the act of willfully ending ones own life. ... A mood disorder is a condition whereby the prevailing emotional mood is distorted or inappropriate to the circumstances. ...

## Notes

•   1. Max Planck, p. 119.
•   2. The concept of entropy was introduced by Rudolf Clausius in 1865. He was the first to enunciate the second law of thermodynamics by saying that entropy always increases.
•   3. An alternative is the information entropy definition introduced in 1948 by Claude Shannon.[6] It was intended for use in communication theory, but is applicable in all areas. It reduces to Boltzmann's expression when all the probabilities are equal, but can, of course, be used when they are not. Its virtue is that it yields immediate results without resorting to factorials or Stirling's approximation. Similar formulas are found, however, as far back as the work of Boltzmann, and explicitly in Gibbs (see reference).
•   4. Wallace Carothers, who discovered neoprene and nylon and founded the science of long-chain polymers, finally drank his cocktail of cyanide-laced lemon juice in 1937, one year before nylon reached the market.
•   5. See Tolman, Chapter VI, for an extensive discussion.
•   6.A memorial activity and discussion meeting on Lattice Boltzmann methods may be held in September, 2006. The Lattice Boltzmann Method is a new method in Computational fluid dynamics which utilities the theories of Boltzmann.

In thermodynamics, entropy, symbolized by S, is a state function of a thermodynamic system defined by the differential quantity , where dQ is the amount of heat absorbed in a reversible process in which the system goes from the one state to another, and T is the absolute temperature. ... Rudolf Clausius - physicist and mathematician Rudolf Julius Emanuel Clausius (January 2, 1822 â€“ August 24, 1888), was a German physicist and mathematician. ... The second law of thermodynamics states that which is equivalent to this scientific statement: The Second Law is a statistical law and thus applicable only to macroscopic systems. ... Entropy of a Bernoulli trial as a function of success probability, often called the binary entropy function. ... Claude Shannon Claude Elwood Shannon (April 30, 1916 â€“ February 24, 2001), an American electrical engineer and mathematician, has been called the father of information theory, and was the founder of practical digital circuit design theory. ... In mathematics, the factorial of a natural number n is the product of all positive integers less than or equal to n. ... The relative difference between (ln x!) and (x ln x - x) approaches zero as x increases. ... In thermodynamics, the H-theorem describes the increase of entropy of an ideal gas in an irreversible process, solving the Boltzmann equation. ... Dr. Wallace Hume Carothers (April 27, 1896 - April 29, 1937) was the leader of organic chemistry at DuPont. ... Neoprene is the DuPont Chemical trade name for a family of synthetic rubbers based on polychloroprene. ... Nylon represents a family of synthetic polymers, a thermoplastic material, first produced on 28 February, 1935 by Gerard J. Berchet of Wallace Carothers research group at DuPont. ... Look up chain in Wiktionary, the free dictionary. ... Polymer is a term used to describe a very long molecule consisting of structural units and repeating units connected by covalent chemical bonds. ... A space-filling model of the cyanide ion A cyanide is any chemical compound that contains the cyano group -Câ‰¡N, with the carbon atom triple-bonded to the nitrogen atom. ... Marketing is a social and managerial function associated with the process of researching, developing, promoting, selling, and distributing a product or service. ... Instead of solving the Navier-Stokes equations, the discrete Boltzmann equation is solved to simulate the flow of Newtonian fluid. ... Computational fluid dynamics (CFD) is the use of computers to analyze problems in fluid dynamics. ...

This is a list of Austrian scientists. ... The following list is an election of famous Austrians. ...

Results from FactBites:

 Ludwig Boltzmann - Wikipedia, the free encyclopedia (1914 words) Ludwig Edward Boltzmann was born on February 20, 1844 in Vienna. Boltzmann was appointed to the Chair of Theoretical Physics at the University of Munich in Bavaria, Germany in 1890. Thus in 1900 Boltzmann went to the University of Leipzig, on the invitation of Wilhelm Ostwald.
 Boltzmann constant - Wikipedia, the free encyclopedia (1217 words) It is named after the Austrian physicist Ludwig Boltzmann, who made important contributions to the theory of statistical mechanics, in which this constant plays a crucial role. Although Boltzmann first linked entropy and probability in 1877, it seems the relation was never expressed with a specific constant until Max Planck first introduced k, and gave an accurate value for it, in his derivation of the law of fl body radiation in December 1900. Before 1900, equations involving Boltzmann factors were not written using the energies per molecule and Boltzmann's constant, but rather using the gas constant R, and macroscopic energies for macroscopic quantities of the substance; as for convenience is still generally the case in Chemistry to this day.
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