Infobox scientist name PaulEhrenfest image Paul Ehrenfest.jpg image size 150px caption birth date Birth ... Afanasyeva . He was the father of the mathematician Tatyana Pavlovna Ehrenfest . PaulEhrenfest ... mechanics , including the theory of phase transition and the Ehrenfest theorem . Biography Paul ... , PaulEhrenfest, Ralph Kronig , and Enrico Fermi In his lectures he would focus on simple models ... , Werner Heisenberg , Paul Dirac , and David M. Dennison David Dennison . Research Most of Ehrenfest ... page 60 chapter PaulEhrenfest ref References reflist Niels Bohr , 1949, http www.tu harburg.de ... , 1970. PaulEhrenfest . Amsterdam. , 1981, http www.phys.uu.nl boeyink ehrenfest images centennial klein.pdf Not by Discoveries Alone the Centennial of PaulEhrenfest, Physica 106A 3 14. Kramers, H ... of Professor PaulEhrenfest, American Journal of Physics 24 431 433. references External links Wikisourceauthor commons PaulEhrenfest H.B.G. Casimir, http www.inghist.nl Onderzoek Projecten BWN lemmata bwn1 ehrenfestEhrenfest, Paul 1880 1933 , in Biografisch Woordenboek van Nederland in Dutch ..., http www.lup.nl do.php?a show visitor book&isbn 9789087281229 PaulEhrenfest. Worstelingen ... van het drama Wetenschappelijke worstelingen van PaulEhrenfest tussen 1916 1925 , master s thesis ... Extras Ehrenfest Collected papers.html Preface to Collected Papers of PaulEhrenfest Frans van Lunteren, http www.phys.uu.nl boeyink ehrenfest images Ehrenfest2.doc PaulEhrenfest de Leidse onderzoekschool ... www.studenten city.de bibliothek wissenschaftler.php?action show&id 74 PaulEhrenfest in Das Lexikon ... Metadata see Wikipedia Persondata . NAME Ehrenfest, Paul ALTERNATIVE NAMES SHORT DESCRIPTION DATE ... Amsterdam DEFAULTSORT Ehrenfest, Paul Category 1880 births Category 1933 deaths Category Austrian ... who committed suicide cs PaulEhrenfest da PaulEhrenfest de PaulEhrenfest el es PaulEhrenfest fr PaulEhrenfest gl PaulEhrenfest it PaulEhrenfest ht PaulEhrenfest nl Paul ... more details
Ehrenfest is a surname which may refer to PaulEhrenfest , a Jewish Austrian physicist and mathematician Ehrenfest equations Ehrenfest model Ehrenfest paradox and Ehrenfest theorem , named after him Ehrenfest theorem 32796 Ehrenfest Tatyana Afanasyeva Tatjana Ehrenfest Afanassjewa , an Ukrainian Russian mathematician, wife of Paul Tatyana Pavlovna Ehrenfest Tanja van Aardenne Ehrenfest 1905 1984 , an Austrian Dutch mathematician, daughter of Paul See also Ehrenfeld disambiguation Ehrenfels disambiguation Ehrenbaum Ehrenberg disambiguation Ehrenburg disambiguation Ehrenhaft Ehrenpreis Ehrenstein disambiguation Ehrenthal disambig surname Category German language surnames Category Jewish surnames de Ehrenfest nl Ehrenfest ... more details
32796 Ehrenfest provisional designation 1990 ET sub 2 sub is a asteroid belt main belt minor planet . It was discovered by Eric Walter Elst at the La Silla Observatory in Chile on March 2, 1990. It is named after PaulEhrenfest , an Austrian Dutch physicist and mathematician of the 19th and 20th centuries. See also List of minor planets 32001&ndash 33000 External links JPL Small Body Beltasteroid stub Minor planets navigator 32795 1989 WA3 32797 1990 OJ Small Solar System bodies DEFAULTSORT Ehrenfest Category Asteroids named for people Category Astronomical objects discovered in 1990 Category Discoveries by Eric Walter Elst fa it 32796 Ehrenfest ... more details
The Ehrenfest model of diffusion was proposed by PaulEhrenfest to explain the second law of thermodynamics . The model considers N particles in two containers. Particles independently change container at a rate . If X t i is defined to be the number of particles in one container at time t, then it is a birth death process with Continuous time Markov process Mathematical definitions transition rates math q i, i 1 i , lambda math for i 1,2,...,N math q i, i 1 N i , lambda math for i 0,1,...,N 1 and equilibrium distribution math pi i 2 N tbinom Ni math . It can be shown that if the initial system state is not equilibrium, then the Entropy information theory entropy , given by math H t sum i P X t i log left frac P X t i pi i right , math is monotonically increasing H theorem . This is a consequence of the convergence to the equilibrium distribution. References F.P. Kelly Reversibility and Stochastic Networks Wiley, Chichester, 1979 ISBN 0471276014 http www.statslab.cam.ac.uk frank BOOKS kelly book.html pp.17 20 Ehrenfest model of diffusion. Encyclop dia Britannica 2008 Category Queueing theory Category Diffusion fr Mod le des urnes d Ehrenfest it Modello di Ehrenfest ... more details
PaulEhrenfestEhrenfest equations equations which describe changes in specific heat capacity and derivatives of specific volume in second order phase transitions . Clausius Clapeyron relation does not make sense for second order phase transitions ref Sivuhin D.V. General physics course. V.2. Thermodynamics and molecular physics. 2005 ref , as both specific heat capacity and specific volume do not change in second order phase transitions. Quantitative consideration Ehrenfest equations are the consequence of continuity of specific entropy math s math and specific volume math v math , which are first derivatives of specific Gibbs free energy in second order phase transitions. If we consider specific entropy math s math as a function of temperature and pressure , then its differential of a function differential is math ds left partial s over partial T right P dT left partial s over partial P right T dP math . As math left partial s over partial T right P c P over T , left partial s over partial P right T left partial v over partial T right P math , then differential of specific entropy also is math d s i c i P over T dT left partial v i over partial T right P dP math Where math i 1 math and math i 2 math are the two phases which transit one into other. Due to continuity of specific entropy, the following holds in second order phase transitions math ds 1 ds 2 math . So, math left c 2P c 1P right dT over T left left partial v 2 over partial T right P left partial v 1 over partial T right P right dP math Therefore, the first Ehrenfest equation math Delta c P T cdot Delta left left partial v over partial T right P right cdot dP over dT math The second Ehrenfest equation is got in a like ... of metals can t be described by Ehrenfest equations. See also PaulEhrenfest Clausius Clapeyron ... Ehrenfest equation is got in a like manner, but specific entropy is considered as function of math ... T math and math P math gives the fourth Ehrenfest equation math Delta left partial v over partial ... more details
Quantum mechanics cTopic Fundamental concepts The Ehrenfest theorem , named after PaulEhrenfest , the Austrian physicist and mathematician, relates the time derivative of the Expectation value quantum mechanics expectation value for a Quantum mechanics quantum mechanical operator physics operator to the commutator of that operator with the Hamiltonian quantum mechanics Hamiltonian of the system. It is math frac d dt langle A rangle frac 1 i hbar langle A,H rangle left langle frac partial A partial t right rangle math where A is some QM operator and math langle A rangle math is its expectation value. Ehrenfest s theorem is obvious in the Heisenberg picture of quantum mechanics, where it is just the expectation value of the Heisenberg equation of motion. Ehrenfest s theorem is closely related to Liouville s theorem Hamiltonian Liouville s theorem from Hamiltonian mechanics , which involves the Poisson bracket instead of a commutator. In fact, it is a rule of thumb that a theorem in quantum mechanics which contains a commutator can be turned into a theorem in classical mechanics by changing the commutator into a Poisson bracket and multiplying by math i hbar math . This causes the operator expectation values to obey their corresponding classical equations of motion provided the Hamiltonian is at most quadratic in the coordinates and momenta. Otherwise, the equations still may hold approximately, provided fluctuations are small. Derivation Suppose some system is presently in a quantum state math Phi math . If we want to know the instantaneous time derivative of the expectation value of A, that is, by definition math frac d dt langle A rangle frac d dt int Phi A Phi dx 3 int left ... math p math . Using Ehrenfest s theorem, we have math frac d dt langle p rangle frac 1 i hbar ... Ehrenfestovy teor my de Ehrenfest Theorem el es Teorema de Ehrenfest fr Th or me d Ehrenfest it Teorema di Ehrenfest ja pl Twierdzenie Ehrenfesta pt Teorema de Ehrenfest ... more details
relativity. ref name Born 1909 After studying Born s notion of rigidity, PaulEhrenfest demonstrated ... claims that Ehrenfest was right, not Einstein. 1935 Paul Langevin essentially introduces a moving ...Inappropriate tone date April 2009 Expert subject Physics date November 2008 The Ehrenfest paradox concerns the rotation of a rigid disc in the theory of relativity . In its original formulation as presented by PaulEhrenfest 1909 in the Physikalische Zeitschrift , ref name Ehren it discusses an ideally rigid cylinder that is made to rotate about its axis of symmetry. The radius R as seen in the laboratory frame is always perpendicular to its motion and should therefore be equal to its value R sub 0 sub when stationary. However, the circumference 2 R should appear Length contraction Lorentz contracted to a smaller value than at rest, by the usual factor . This leads to the contradiction that R R sub 0 sub and R R sub 0 sub . Note that a cylinder was considered in order to circumvent the possibility ..., which would thus measure greater than 2 R. The Ehrenfest paradox may be the most basic phenomenon in relativity ... angular velocity math omega math . Image ehrenfest paradox diagram.svg thumb right Ehrenfest ... it should be exactly equal to math pi math . Ehrenfest s argument Ehrenfest considered an ideally Born ... contraction the discrepancy noted by Ehrenfest seems to suggest that a rotated Born rigid disk should shatter. Thus Ehrenfest argued by reductio ad absurdum that Born rigidity is not generally compatible ... from a state of rest into rotation, confirming Ehrenfest s result. ref name Herg ref name Noeth ... Electron in the Kinematics of the Principle of Relativity ref ref name Ehren cite journal author Ehrenfest ... by yvind Gr n, on which the brief history in this article is based, and some other papers on the Ehrenfest ... Physical paradoxes cs Ehrenfest v paradox de Ehrenfestsches Paradoxon fr Paradoxe d Ehrenfest hu Ehrenfest paradoxon nl Ehrenfest paradox pl Paradoks Ehrenfesta ru sl Ehrenfestov ... more details
The Ehrenfest Tolman effect also known as the Tolman Ehrenfest effect , created by Richard Chase Tolman Richard C. Tolman and PaulEhrenfest , argues that temperature is not constant in space at thermal equilibrium , but varies with the spacetime curvature. Specifically, it depends on the spacetime metric. In a stationary spacetime with timelike Killing vector field math xi math , the temperature math T math satisfies instead the Tolman Ehrenfest relation math T , xi mathrm constant math . This relationship leads to the concept of thermal time which has been considered as a possible basis for a fully general relativistic thermodynamics. It has been shown that the Tolman Ehrenfest effect can be derived by applying the equivalence principle to the concept that temperature is the rate of thermal time with respect to proper time. ref http arxiv.org abs 1005.2985arxiv.org abs 1005.2985 Rovelli & Smerlak, 2010, Classical and Quantum Gravity, 28, 4 ref References references quantum stub Category Quantum mechanics ... more details
File Tatyana van Aardenne Ehrenfest.jpg thumb van Aardenne Ehrenfest in 1977 br Photo courtesy of Mathematical Research Institute of Oberwolfach MFO Tatyana Pavlovna Ehrenfest , later van Aardenne Ehrenfest , Vienna , October 28, 1905 &ndash Dordrecht , November 29, 1984 was a Netherlands Dutch mathematician . She was the daughter of PaulEhrenfest 1880 &ndash 1933 and Tatyana Afanasyeva Tatyana Alexeyevna Afanasyeva 1876&ndash 1964 . Tatyana Ehrenfest was born in Vienna, and spent her childhood in Saint Petersburg St Petersburg . In 1912 the Ehrenfests moved to Leiden where her father succeeded Hendrik Lorentz H.A. Lorentz as professor at the Leiden University University of Leiden . Until 1917 she was home schooled, after that she attended the Stedelijk Gymnasium Leiden Gymnasium in Leiden and passed the Gymnasium school Final degree final exams in 1922. She studied mathematics and physics at the University of Leiden. In 1928 she went to G ttingen where she took courses from Harald Bohr and Max Born . On December 8, 1931 she obtained her Ph.D. in Leiden. ref thesis Under her married name, Tanja van Aardenne Ehrenfest, she is known for her contributions to De Bruijn sequence s, the Van der Corput sequence discrepancy theorem ref Weisstein and the BEST theorem . References note thesis Oppervlakken met scharen van gesloten geodetische lijnen , Thesis, Leiden, 1931. note Weisstein Eric W. Weisstein. http mathworld.wolfram.com DiscrepancyTheorem.html Discrepancy Theorem . From MathWorld ... In memoriam T. van Aardenne Ehrenfest, 1905 1984 , Nieuw Archief voor Wiskunde 4 , Vol.3, 1985 235 236. Persondata Metadata see Wikipedia Persondata . NAME Ehrenfest, Tatyana ALTERNATIVE NAMES SHORT ... OF DEATH DEFAULTSORT Ehrenfest, Tatyana Category 1905 births Category 1984 deaths Category 20th century ... descent Netherlands scientist stub Euro mathematician stub fr Tatiana Pavlovna Ehrenfest it Tatjana Pavlovna Ehrenfest nl Tatjana Pavlovna Ehrenfest ... more details
TOCRight Paul may refer to Paul name , a given name or surname includes a list of people with that name People Christianity Paul the Apostle c. 5 c. 67 , also known as Paul of Tarsus or Saint Paul, early Christian missionary and author of much of the New Testament Saint Paul disambiguation , multiple other people and locations named Saint Paul Pope Paul disambiguation , multiple Popes of the Roman Catholic Church Roman and Byzantine empire Lucius Aemilius Paullus Macedonicus c. 229 BC 160 BC , Roman general Julius Paulus Prudentissimus fl. 2nd century AD , Roman jurist Paulus Catena died 362 , Roman notary Paulus Alexandrinus 4th century , Hellenistic astrologer Paul of Aegina or Paulus Aegineta c. 625 c. 690 , Greek surgeon Royals Paul I of Russia 1754 1801 , Tsar of Russia Paul of Greece ... as Paul , see the page Paul name for list of notable Pauls Paolo Giovio or Paulus Jovius 1483 1552 , Italian bishop Paul the Deacon or Paulus Diaconus c. 720 c. 799 , Italian Benedictine monk Places Paul, Cornwall , United Kingdom Paul, Idaho , United States Paul, Cape Verde Other uses Paul bakery , bakery franchise based in France Paul film Paul film , 2011 film with Simon Pegg and Nick Frost Paul play Paul play , play by Howard Brenton Paul song Paul song , by the German punk band Die rzte Paul Pok mon Paul Pok mon , fictional character St. Paul oratorio St. Paul oratorio , work by Felix Mendelssohn originally entitled Paulus in its German version Hurricane Paul 1982 Hurricane Paul 2006 Paul is dead , conspiracy theory about Paul McCartney Paul the Octopus 2008 2010 , an octopus that correctly guessed results in the 2010 World Cup Paul II octopus , the successor of Paul the Octopus Poker Face Paul , a Game Gear video game that comes in blackjack and poker versions See also Paula disambiguation Disambig cs Paul de Paul Begriffskl rung es Paul id Paulus it Paul lt Paulius nl Paul ja ro Paul ru simple Paul sl Paul uk ... more details
. Image EinsteinEhrenfestKamerlingh OnnesWeiss.jpg thumb left upright Albert Einstein , PaulEhrenfest , Paul Langevin, Heike Kamerlingh Onnes , and Pierre Weiss at Ehrenfest s home in Leiden ...Infobox Scientist name Paul Langevin image Langevin.jpg 224px image size 224px caption Paul Langevin 1872 1946 birth date birth date 1872 1 23 df y birth place Paris , France death date death date and age df y 1946 12 19 1872 1 23 death place Paris , France residence France nationality France French field Physics work institution University of Cambridge br Coll ge de France br Sorbonne br ESPCI alma mater ESPCI br cole Normale Sup rieure doctoral advisor Pierre Curie doctoral students Ir ne Joliot Curie known for Langevin equation prizes Hughes Medal 1915 br Copley Medal 1940 religion footnotes Paul Langevin 23 January 1872 &ndash 19 December 1946 was a prominent France French physicist ... for most of the war. Paul Langevin, previously a doctoral student of Pierre Curie and later ... 187.full ref However the war was over by the time he had it operational. During his career, Paul Langevin ... of piezoelectric transducers for the goal of submarine detection a Paul Langevin, b Robert William ... Paul Langevin and Chilowski filed two US patents disclosing the first ultrasonic submarine detector ..., 1995, ISBN 0 434 60503 4. External links commons Paul Langevin http scienceworld.wolfram.com ...?browse people Langevin, Paul Annotated bibliography for Niels Bohr from the Alsos Digital ... NAME Langevin, Paul ALTERNATIVE NAMES SHORT DESCRIPTION France French Physicist DATE OF BIRTH 23 January ... DEFAULTSORT Langevin, Paul Category 1872 births Category 1946 deaths Category Alumni of the cole Normale ... ca Paul Langevin cs Paul Langevin de Paul Langevin el es Paul Langevin fr Paul Langevin it Paul Langevin ht Paul Langevin nl Paul Langevin ja pl Paul Langevin pt Paul Langevin ro Paul Langevin ru , sk Paul Langevin sl Paul Langevin fi Paul Langevin tr Paul Langevin ... more details
Paul Friedl nder may refer to Paul Friedlaender chemist Paul Friedl nder philologist hndis Friedl nder, Paul de Paul Friedl nder sv Paul Friedl nder ... more details
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