This article needs additional citations for verification .(August 2010) |

Thermodynamics |
---|

A timeline of events in the history of thermodynamics.

- 1650 – Otto von Guericke builds the first vacuum pump
- 1660 – Robert Boyle experimentally discovers Boyle's Law, relating the pressure and volume of a gas (published 1662)
^{ [1] } - 1665 – Robert Hooke published his book
*Micrographia*, which contained the statement: "Heat being nothing else but a very brisk and vehement agitation of the parts of a body."^{ [2] } - 1667 – J. J. Becher puts forward a theory of combustion involving
*combustible earth*in his book*Physica subterranea*^{ [3] }(see Phlogiston theory). - 1676–1689 – Gottfried Leibniz develops the concept of
*vis viva*, a limited version of the conservation of energy - 1679 – Denis Papin designed a steam digester which inspired the development of the piston-and-cylinder steam engine.
- 1694–1734 – Georg Ernst Stahl names Becher's combustible earth as phlogiston and develops the theory
- 1698 – Thomas Savery patents an early steam engine
^{ [4] } - 1702 – Guillaume Amontons introduces the concept of absolute zero, based on observations of gases
- 1738 – Daniel Bernoulli publishes
*Hydrodynamica*, initiating the kinetic theory - 1749 – Émilie du Châtelet, in her French translation and commentary on Newton's
*Philosophiae Naturalis Principia Mathematica*, derives the conservation of energy from the first principles of Newtonian mechanics. - 1761 – Joseph Black discovers that ice absorbs heat without changing its temperature when melting
- 1772 – Black's student Daniel Rutherford discovers nitrogen,
^{ [5] }^{ [6] }which he calls*phlogisticated air*, and together they explain the results in terms of the phlogiston theory - 1776 – John Smeaton publishes a paper on experiments related to power, work, momentum, and kinetic energy, supporting the conservation of energy
- 1777 – Carl Wilhelm Scheele distinguishes heat transfer by thermal radiation from that by convection and conduction
- 1783 – Antoine Lavoisier discovers oxygen and develops an explanation for combustion; in his paper "Réflexions sur le phlogistique", he deprecates the phlogiston theory and proposes a caloric theory
- 1784 – Jan Ingenhousz describes Brownian motion of charcoal particles on water
- 1791 – Pierre Prévost shows that all bodies radiate heat, no matter how hot or cold they are
^{ [7] } - 1798 – Count Rumford (Benjamin Thompson) publishes his paper
*An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction*detailing measurements of the frictional heat generated in boring cannons and develops the idea that heat is a form of kinetic energy; his measurements are inconsistent with caloric theory, but are also sufficiently imprecise as to leave room for doubt.

- 1802 – Joseph Louis Gay-Lussac publishes Charles's law, discovered (but unpublished) by Jacques Charles around 1787; this shows the dependency between temperature and volume. Gay-Lussac also formulates the law relating temperature with pressure (the pressure law, or Gay-Lussac's law)
- 1804 – Sir John Leslie observes that a matte black surface radiates heat more effectively than a polished surface, suggesting the importance of black-body radiation
- 1805 – William Hyde Wollaston defends the conservation of energy in
*On the Force of Percussion* - 1808 – John Dalton defends caloric theory in
*A New System of Chemistry*and describes how it combines with matter, especially gases; he proposes that the heat capacity of gases varies inversely with atomic weight - 1810 – Sir John Leslie freezes water to ice artificially
- 1813 – Peter Ewart supports the idea of the conservation of energy in his paper
*On the measure of moving force*; the paper strongly influences Dalton and his pupil, James Joule - 1819 – Pierre Louis Dulong and Alexis Thérèse Petit give the Dulong-Petit law for the specific heat capacity of a crystal
- 1820 – John Herapath develops some ideas in the kinetic theory of gases but mistakenly associates temperature with molecular momentum rather than kinetic energy; his work receives little attention other than from Joule
- 1822 – Joseph Fourier formally introduces the use of dimensions for physical quantities in his
*Théorie Analytique de la Chaleur* - 1822 – Marc Seguin writes to John Herschel supporting the conservation of energy and kinetic theory
- 1824 – Sadi Carnot analyzes the efficiency of steam engines using caloric theory; he develops the notion of a reversible process and, in postulating that no such thing exists in nature, lays the foundation for the second law of thermodynamics, and initiating the science of thermodynamics
- 1827 – Robert Brown discovers the Brownian motion of pollen and dye particles in water
^{ [8] } - 1831 – Macedonio Melloni demonstrates that black-body radiation can be reflected, refracted, and polarised in the same way as light
- 1834 – Émile Clapeyron popularises Carnot's work through a graphical and analytic formulation. He also combined Boyle's Law, Charles's Law, and Gay-Lussac's Law to produce a Combined Gas Law. PV/T = k
^{ [9] } - 1841 – Julius Robert von Mayer, an amateur scientist, writes a paper on the conservation of energy, but his lack of academic training leads to its rejection
- 1842 – Mayer makes a connection between work, heat, and the human metabolism based on his observations of blood made while a ship's surgeon; he calculates the mechanical equivalent of heat
- 1842 – William Robert Grove demonstrates the thermal dissociation of molecules into their constituent atoms, by showing that steam can be disassociated into oxygen and hydrogen, and the process reversed
- 1843 – John James Waterston fully expounds the kinetic theory of gases,
^{ [10] }but according to D Levermore "there is no evidence that any physical scientist read the book; perhaps it was overlooked because of its misleading title, Thoughts on the Mental Functions."^{ [11] } - 1843 – James Joule experimentally finds the mechanical equivalent of heat
^{ [12] } - 1845 – Henri Victor Regnault added Avogadro's Law to the Combined Gas Law to produce the Ideal Gas Law. PV = nRT
- 1846 – Grove publishes an account of the general theory of the conservation of energy in
*On The Correlation of Physical Forces*^{ [13] } - 1847 – Hermann von Helmholtz publishes a definitive statement of the conservation of energy, the first law of thermodynamics
^{ [14] }

- 1848 – William Thomson extends the concept of absolute zero from gases to all substances
- 1849 – William John Macquorn Rankine calculates the correct relationship between saturated vapour pressure and temperature using his
*hypothesis of molecular vortices* - 1850 – Rankine uses his
*vortex*theory to establish accurate relationships between the temperature, pressure, and density of gases, and expressions for the latent heat of evaporation of a liquid; he accurately predicts the surprising fact that the apparent specific heat of saturated steam will be negative - 1850 – Rudolf Clausius coined the term "entropy" (das Wärmegewicht, symbolized S) to denote heat lost or turned into waste. ("Wärmegewicht" translates literally as "heat-weight"; the corresponding English term stems from the Greek τρέπω, "I turn".)
- 1850 – Clausius gives the first clear joint statement of the first and second law of thermodynamics, abandoning the caloric theory, but preserving Carnot's principle
- 1851 – Thomson gives an alternative statement of the second law
- 1852 – Joule and Thomson demonstrate that a rapidly expanding gas cools, later named the Joule–Thomson effect or Joule–Kelvin effect
- 1854 – Helmholtz puts forward the idea of the heat death of the universe
- 1854 – Clausius establishes the importance of
*dQ/T*(Clausius's theorem), but does not yet name the quantity - 1854 – Rankine introduces his
*thermodynamic function*, later identified as entropy - 1856 – August Krönig publishes an account of the kinetic theory of gases, probably after reading Waterston's work
- 1857 – Clausius gives a modern and compelling account of the kinetic theory of gases in his
*On the nature of motion called heat* - 1859 – James Clerk Maxwell discovers the distribution law of molecular velocities
- 1859 – Gustav Kirchhoff shows that energy emission from a black body is a function of only temperature and frequency
- 1862 – "Disgregation", a precursor of entropy, was defined in 1862 by Clausius as the magnitude of the degree of separation of molecules of a body
- 1865 – Clausius introduces the modern macroscopic concept of entropy
- 1865 – Josef Loschmidt applies Maxwell's theory to estimate the number-density of molecules in gases, given observed gas viscosities.
- 1867 – Maxwell asks whether Maxwell's demon could reverse irreversible processes
- 1870 – Clausius proves the scalar virial theorem
- 1872 – Ludwig Boltzmann states the Boltzmann equation for the temporal development of distribution functions in phase space, and publishes his H-theorem
- 1873 - Johannes Diderik van der Waals formulates his equation of state
- 1874 – Thomson formally states the second law of thermodynamics
- 1876 – Josiah Willard Gibbs publishes the first of two papers (the second appears in 1878) which discuss phase equilibria, statistical ensembles, the free energy as the driving force behind chemical reactions, and chemical thermodynamics in general.
^{[ citation needed ]} - 1876 – Loschmidt criticises Boltzmann's H theorem as being incompatible with microscopic reversibility (Loschmidt's paradox).
- 1877 – Boltzmann states the relationship between entropy and probability
- 1879 – Jožef Stefan observes that the total radiant flux from a blackbody is proportional to the fourth power of its temperature and states the Stefan–Boltzmann law
- 1884 – Boltzmann derives the Stefan–Boltzmann blackbody radiant flux law from thermodynamic considerations
- 1888 – Henri-Louis Le Chatelier states his principle that the response of a chemical system perturbed from equilibrium will be to counteract the perturbation
- 1889 – Walther Nernst relates the voltage of electrochemical cells to their chemical thermodynamics via the Nernst equation
- 1889 – Svante Arrhenius introduces the idea of activation energy for chemical reactions, giving the Arrhenius equation
- 1893 – Wilhelm Wien discovers the displacement law for a blackbody's maximum specific intensity

- 1900 – Max Planck suggests that light may be emitted in discrete frequencies, giving his law of black-body radiation
^{ [15] } - 1905 – Albert Einstein, in the first of his miracle year papers, argues that the reality of quanta would explain the photoelectric effect
^{ [16] } - 1905 – Einstein mathematically analyzes Brownian motion as a result of random molecular motion in his paper On the movement of small particles suspended in a stationary liquid demanded by the molecular-kinetic theory of heat
- 1906 – Nernst presents a formulation of the third law of thermodynamics
- 1907 – Einstein uses quantum theory to estimate the heat capacity of an Einstein solid
- 1909 – Constantin Carathéodory develops an axiomatic system of thermodynamics
^{ [17] } - 1910 – Einstein and Marian Smoluchowski find the Einstein–Smoluchowski formula for the attenuation coefficient due to density fluctuations in a gas
- 1911 – Paul Ehrenfest and Tatjana Ehrenfest–Afanassjewa publish their classical review on the statistical mechanics of Boltzmann,
*Begriffliche Grundlagen der statistischen Auffassung in der Mechanik* - 1912 – Peter Debye gives an improved heat capacity estimate by allowing low-frequency phonons
^{ [18] } - 1916 – Sydney Chapman and David Enskog systematically develop the kinetic theory of gases.
- 1916 – Einstein considers the thermodynamics of atomic spectral lines and predicts stimulated emission
- 1919 – James Jeans discovers that the dynamical constants of motion determine the distribution function for a system of particles
- 1920 – Meghnad Saha states his ionization equation
^{ [19] } - 1923 – Debye and Erich Hückel publish a statistical treatment of the dissociation of electrolytes
- 1924 – Satyendra Nath Bose introduces Bose–Einstein statistics, in a paper translated by Einstein
- 1926 – Enrico Fermi
^{ [20] }and Paul Dirac^{ [21] }introduce Fermi–Dirac statistics - 1927 – John von Neumann introduces the density matrix representation,
^{ [22] }establishing quantum statistical mechanics - 1928 – John B. Johnson discovers Johnson noise in a resistor
^{ [23] }^{ [24] } - 1928 – Harry Nyquist derives the fluctuation-dissipation theorem, a relationship to explain Johnson noise in a resistor
^{ [25] } - 1931 – Lars Onsager publishes his groundbreaking paper deriving the Onsager reciprocal relations
^{ [26] } - 1938 – Anatoly Vlasov proposes the Vlasov equation for a correct dynamical description of ensembles of particles with collective long range interaction.
^{ [27] }^{ [28] } - 1939 – Nikolay Krylov and Nikolay Bogolyubov give the first consistent microscopic derivation of the Fokker–Planck equation in the single scheme of classical and quantum mechanics
^{ [29] }^{ [30] } - 1942 – Joseph L. Doob states his theorem on Gauss–Markov processes
- 1944 – Lars Onsager gives an analytic solution to the 2-dimensional Ising model, including its phase transition
^{ [31] }

- 1945–1946 – Nikolay Bogoliubov develops a general method for a microscopic derivation of kinetic equations for classical statistical systems using BBGKY hierarchy
^{ [32] }^{ [33] } - 1947 – Nikolay Bogoliubov and Kirill Gurov extend this method for a microscopic derivation of kinetic equations for quantum statistical systems
- 1948 – Claude Elwood Shannon establishes information theory
^{ [34] } - 1957 – Aleksandr Solomonovich Kompaneets derives his Compton scattering Fokker–Planck equation
- 1957 – Ryogo Kubo derives the first of the Green-Kubo relations for linear transport coefficients
^{ [35] } - 1957 – Edwin T. Jaynes publishes two papers detailing the MaxEnt interpretation of thermodynamics from information theory
^{ [36] }^{ [37] } - 1960–1965 – Dmitry Zubarev develops the method of non-equilibrium statistical operator, which becomes a classical tool in the statistical theory of non-equilibrium processes
- 1972 – Jacob Bekenstein suggests that black holes have an entropy proportional to their surface area
- 1974 – Stephen Hawking predicts that black holes will radiate particles with a black-body spectrum which can cause black hole evaporation
- 1977 – Ilya Prigogine wins the Nobel prize for his work on dissipative structures in thermodynamic systems far from equilibrium. The importation and dissipation of energy could reverse the 2nd law of thermodynamics

In physics, **energy** is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units (SI) is the joule (J).

**Entropy** is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change, and information systems including the transmission of information in telecommunication.

In physics, **statistical mechanics** is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles.

**Thermodynamics** is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, biochemistry, chemical engineering and mechanical engineering, but also in other complex fields such as meteorology.

The **second law of thermodynamics** is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects, unless energy in some form is supplied to reverse the direction of heat flow. Another definition is: "Not all heat energy can be converted into work in a cyclic process."

Certain systems can achieve **negative thermodynamic temperature**; that is, their temperature can be expressed as a negative quantity on the Kelvin or Rankine scales. This should be distinguished from temperatures expressed as negative numbers on non-thermodynamic Celsius or Fahrenheit scales, which are nevertheless higher than absolute zero.

In classical statistical mechanics, the ** H-theorem**, introduced by Ludwig Boltzmann in 1872, describes the tendency to decrease in the quantity

**Non-equilibrium thermodynamics** is a branch of thermodynamics that deals with physical systems that are not in thermodynamic equilibrium but can be described in terms of macroscopic quantities that represent an extrapolation of the variables used to specify the system in thermodynamic equilibrium. Non-equilibrium thermodynamics is concerned with transport processes and with the rates of chemical reactions.

**Ludwig Eduard Boltzmann** was an Austrian physicist and philosopher. His greatest achievements were the development of statistical mechanics, and the statistical explanation of the second law of thermodynamics. In 1877 he provided the current definition of entropy, , where Ω is the number of microstates whose energy equals the system's energy, interpreted as a measure of statistical disorder of a system. Max Planck named the constant *k*_{B} the Boltzmann constant.

In science, a process that is not reversible is called **irreversible**. This concept arises frequently in thermodynamics. All complex natural processes are irreversible, although a phase transition at the coexistence temperature is well approximated as reversible.

The **laws of thermodynamics** are a set of scientific laws which define a group of physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems in thermodynamic equilibrium. The laws also use various parameters for thermodynamic processes, such as thermodynamic work and heat, and establish relationships between them. They state empirical facts that form a basis of precluding the possibility of certain phenomena, such as perpetual motion. In addition to their use in thermodynamics, they are important fundamental laws of physics in general, and are applicable in other natural sciences.

The **history of thermodynamics** is a fundamental strand in the history of physics, the history of chemistry, and the history of science in general. Owing to the relevance of thermodynamics in much of science and technology, its history is finely woven with the developments of classical mechanics, quantum mechanics, magnetism, and chemical kinetics, to more distant applied fields such as meteorology, information theory, and biology (physiology), and to technological developments such as the steam engine, internal combustion engine, cryogenics and electricity generation. The development of thermodynamics both drove and was driven by atomic theory. It also, albeit in a subtle manner, motivated new directions in probability and statistics; see, for example, the timeline of thermodynamics.

The mathematical expressions for thermodynamic entropy in the statistical thermodynamics formulation established by Ludwig Boltzmann and J. Willard Gibbs in the 1870s are similar to the information entropy by Claude Shannon and Ralph Hartley, developed in the 1940s.

The principle of **microscopic reversibility** in physics and chemistry is twofold:

The concept of **entropy** developed in response to the observation that a certain amount of functional energy released from combustion reactions is always lost to dissipation or friction and is thus not transformed into useful work. Early heat-powered engines such as Thomas Savery's (1698), the Newcomen engine (1712) and the Cugnot steam tricycle (1769) were inefficient, converting less than two percent of the input energy into useful work output; a great deal of useful energy was dissipated or lost. Over the next two centuries, physicists investigated this puzzle of lost energy; the result was the concept of entropy.

This timeline lists significant discoveries in physics and the laws of nature, including experimental discoveries, theoretical proposals that were confirmed experimentally, and theories that have significantly influenced current thinking in modern physics. Such discoveries are often a multi-step, multi-person process. Multiple discovery sometimes occurs when multiple research groups discover the same phenomenon at about the same time, and scientific priority is often disputed. The listings below include some of the most significant people and ideas by date of publication or experiment.

This article is a summary of common equations and quantities in thermodynamics.

**Temperature** is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.

**Energy dissipation and entropy production extremal principles** are ideas developed within non-equilibrium thermodynamics that attempt to predict the likely steady states and dynamical structures that a physical system might show. The search for extremum principles for non-equilibrium thermodynamics follows their successful use in other branches of physics. According to Kondepudi (2008), and to Grandy (2008), there is no general rule that provides an extremum principle that governs the evolution of a far-from-equilibrium system to a steady state. According to Glansdorff and Prigogine, irreversible processes usually are not governed by global extremal principles because description of their evolution requires differential equations which are not self-adjoint, but local extremal principles can be used for local solutions. Lebon Jou and Casas-Vásquez (2008) state that "In non-equilibrium ... it is generally not possible to construct thermodynamic potentials depending on the whole set of variables". Šilhavý (1997) offers the opinion that "... the extremum principles of thermodynamics ... do not have any counterpart for [non-equilibrium] steady states ." It follows that any general extremal principle for a non-equilibrium problem will need to refer in some detail to the constraints that are specific for the structure of the system considered in the problem.

The **19th century in science** saw the birth of science as a profession; the term scientist was coined in 1833 by William Whewell, which soon replaced the older term of (natural) philosopher.

- ↑ In 1662, he published a second edition of the 1660 book
*New Experiments Physico-Mechanical, Touching the Spring of the Air, and its Effects*with an addendum*Whereunto is Added a Defence of the Authors Explication of the Experiments, Against the Obiections of Franciscus Linus and Thomas Hobbes*; see*J Appl Physiol*98: 31–39, 2005. (Jap.physiology.org Online.) - ↑ Hooke, Robert, Robert (1965).
*Micrographia*. s.l.: Science Heritage. p. 12. - ↑ Becher, Johann Joachim, 1635-1682. (1738).
*Physica subterranea profundam subterraneorum genesin, e principiis hucusque ignotis, ostendens*. Ex officina Weidmanniana. OCLC 3425904.`{{cite book}}`

: CS1 maint: multiple names: authors list (link) - ↑ Jenkins, Rhys (1936).
*Links in the History of Engineering and Technology from Tudor Times*. Ayer Publishing. p. 66. ISBN 0-8369-2167-4. - ↑ See:
- Daniel Rutherford (1772) "Dissertatio Inauguralis de aere fixo, aut mephitico" (Inaugural dissertation on the air [called] fixed or mephitic), M.D. dissertation, University of Edinburgh, Scotland.
- English translation: Leonard Dobbin (1935) "Daniel Rutherford's inaugural dissertation,"
*Journal of Chemical Education*,**12**(8) : 370–375. - See also: James R. Marshall and Virginia L. Marshall (Spring 2015) "Rediscovery of the Elements: Daniel Rutherford, nitrogen, and the demise of phlogiston,"
*The Hexagon*(of Alpha Chi Sigma),**106**(1) : 4–8. Available on-line at: University of North Texas.

- ↑ Lavoisier, Antoine Laurent (1965).
*Elements of chemistry, in a new systematic order: containing all the modern discoveries*. Courier Dover Publications. p. 15. ISBN 0-486-64624-6. - ↑ Prévost, Pierre (April 1791). "Mémoire sur l'équilibre du feu".
*Observations Sur la Physique*(in French).**XXXVIII**(1): 314–323. - ↑ Brown, Robert, 1773-1858. (1828).
*A brief account of microscopical observations made in the months of June, July, and August, 1827, on the particles contained in the pollen of plants: and on the general existence of active molecules in organic and inorganic bodies ...*A. and C. Black. OCLC 38057036.`{{cite book}}`

: CS1 maint: multiple names: authors list (link) - ↑ CLAPEYRON, Benoît Paul Émile. (1834).
*Mémoire sur la puissance motrice de la chaleur*. OCLC 559435201. - ↑ Waterston, John J. (1843).
*Thoughts on the mental functions : being an attempt to treat metaphysics as a branch of the physiology of the nervous system*. London. OCLC 328092289. - ↑ "Neglected Pioneers".
*www.math.umd.edu*. Retrieved 2020-12-20. - ↑ Joule, J.P. (1843). "LII. On the calorific effects of magneto-electricity, and on the mechanical value of heat".
*The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science*.**23**(154): 435–443. doi:10.1080/14786444308644766. ISSN 1941-5966. - ↑ Grove, W. R. (1874).
*The correlation of physical forces (6th edition) by W.R. Grove*. London: Longmans, Green. doi:10.5962/bhl.title.19475. - ↑ Helmholtz, Hermann v. (1847).
*Über die Erhaltung der Kraft, eine physikalische Abhandlung*. OCLC 488622067. - ↑ Planck, Max, 1858-1947.
*Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum*. OCLC 15745309.`{{cite book}}`

: CS1 maint: multiple names: authors list (link) - ↑ Einstein, Albert (1905). "On a Heuristic Viewpoint Concerning the Production and Transformation of Light" (PDF).
*Annalen der Physik (In German)*. - ↑ Pogliani, Lionello; Berberan-Santos, Mario (2000). "Constantin Carathéodory and the axiomatic thermodynamics" (PDF).
*Journal of Mathematical Chemistry*.**28**(1): 313. doi:10.1023/A:1018834326958. S2CID 17244147 . Retrieved May 30, 2022. - ↑ Debye, Peter (1912). "Zur Theorie der spezifischen Waerme".
*Annalen der Physik*(in German).**39**(4): 789–839. Bibcode:1912AnP...344..789D. doi:10.1002/andp.19123441404. - ↑ Saha, Megh Nad (1920). "LIII.Ionization in the solar chromosphere".
*Philosophical Magazine*. Series 6.**40**(238): 472–488. doi:10.1080/14786441008636148. - ↑ Fermi, Enrico (1926). "Sulla quantizzazione del gas perfetto monoatomico".
*Rendiconti Lincei*(in Italian).**3**: 145–9., translated as Zannoni, Alberto (1999-12-14). "On the Quantization of the Monoatomic Ideal Gas". arXiv: cond-mat/9912229 . - ↑ Dirac, Paul A. M. (1926). "On the Theory of Quantum Mechanics".
*Proceedings of the Royal Society A*.**112**(762): 661–77. Bibcode:1926RSPSA.112..661D. doi: 10.1098/rspa.1926.0133 . JSTOR 94692. - ↑ von Neumann, John (1927), "Wahrscheinlichkeitstheoretischer Aufbau der Quantenmechanik",
*Göttinger Nachrichten*,**1**: 245–272 - ↑ Anonymous (1927). "Minutes of the Philadelphia Meeting December 28, 29, 30, 1926".
*Physical Review*.**29**(2): 350–373. Bibcode:1927PhRv...29..350.. doi:10.1103/PhysRev.29.350. - ↑ Johnson, J. (1928). "Thermal Agitation of Electricity in Conductors".
*Physical Review*.**32**(97): 97–109. Bibcode:1928PhRv...32...97J. doi:10.1103/physrev.32.97. - ↑ Nyquist H (1928). "Thermal Agitation of Electric Charge in Conductors".
*Physical Review*.**32**(1): 110–113. Bibcode:1928PhRv...32..110N. doi:10.1103/PhysRev.32.110. - ↑ Onsager, Lars (1931-02-15). "Reciprocal Relations in Irreversible Processes. I."
*Physical Review*. American Physical Society (APS).**37**(4): 405–426. Bibcode:1931PhRv...37..405O. doi: 10.1103/physrev.37.405 . ISSN 0031-899X. - ↑ A. A. Vlasov (1938). "On Vibration Properties of Electron Gas".
*J. Exp. Theor. Phys.*(in Russian).**8**(3): 291. - ↑ A. A. Vlasov (1968). "The Vibrational Properties of an Electron Gas".
*Soviet Physics Uspekhi*.**10**(6): 721–733. Bibcode:1968SvPhU..10..721V. doi:10.1070/PU1968v010n06ABEH003709. S2CID 122952713. - ↑ N. N. Bogolyubov Jr. and D. P. Sankovich (1994). "N. N. Bogolyubov and statistical mechanics".
*Russian Math. Surveys***49**(5): 19—49. doi : 10.1070/RM1994v049n05ABEH002419 - ↑ N. N. Bogoliubov and N. M. Krylov (1939).
*Fokker–Planck equations generated in perturbation theory by a method based on the spectral properties of a perturbed Hamiltonian*. Zapiski Kafedry Fiziki Akademii Nauk Ukrainian SSR**4**: 81–157 (in Ukrainian). - ↑ Onsager, Lars (1944-02-01). "Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition".
*Physical Review*.**65**(3–4): 117–149. Bibcode:1944PhRv...65..117O. doi:10.1103/physrev.65.117. ISSN 0031-899X. - ↑ N. N. Bogoliubov (1946). "Kinetic Equations".
*Journal of Experimental and Theoretical Physics*(in Russian).**16**(8): 691–702. - ↑ N. N. Bogoliubov (1946). "Kinetic Equations".
*Journal of Physics USSR*.**10**(3): 265–274. - ↑ Shannon, Claude Elwood, 1916-2001. (September 1998).
*The mathematical theory of communication*. ISBN 978-0-252-09803-1. OCLC 967725093.`{{cite book}}`

: CS1 maint: multiple names: authors list (link) - ↑ Kubo, Ryogo (1957-06-15). "Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems".
*Journal of the Physical Society of Japan*.**12**(6): 570–586. doi:10.1143/JPSJ.12.570. ISSN 0031-9015. - ↑ Jaynes, E.T. (1957). "Information theory and statistical mechanics" (PDF).
*Physical Review*.**106**(4): 620–630. Bibcode:1957PhRv..106..620J. doi:10.1103/PhysRev.106.620. - ↑ — (1957). "Information theory and statistical mechanics II" (PDF).
*Physical Review*.**108**(2): 171–190. Bibcode:1957PhRv..108..171J. doi:10.1103/PhysRev.108.171.

This page is based on this Wikipedia article

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.

Text is available under the CC BY-SA 4.0 license; additional terms may apply.

Images, videos and audio are available under their respective licenses.