Citation for this page in APA citation style.

Philosophers
Mortimer Adler Rogers Albritton Alexander of Aphrodisias Samuel Alexander William Alston Anaximander G.E.M.Anscombe Anselm Louise Antony Thomas Aquinas Aristotle David Armstrong Harald Atmanspacher Robert Audi Augustine J.L.Austin A.J.Ayer Alexander Bain Mark Balaguer Jeffrey Barrett William Barrett William Belsham Henri Bergson George Berkeley Isaiah Berlin Richard J. Bernstein Bernard Berofsky Robert Bishop Max Black Susanne Bobzien Emil du Bois-Reymond Hilary Bok Laurence BonJour George Boole Émile Boutroux F.H.Bradley C.D.Broad Michael Burke Lawrence Cahoone C.A.Campbell Joseph Keim Campbell Rudolf Carnap Carneades Ernst Cassirer David Chalmers Roderick Chisholm Chrysippus Cicero Randolph Clarke Samuel Clarke Anthony Collins Antonella Corradini Diodorus Cronus Jonathan Dancy Donald Davidson Mario De Caro Democritus Daniel Dennett Jacques Derrida René Descartes Richard Double Fred Dretske John Dupré John Earman Laura Waddell Ekstrom Epictetus Epicurus Herbert Feigl Arthur Fine John Martin Fischer Frederic Fitch Owen Flanagan Luciano Floridi Philippa Foot Alfred Fouilleé Harry Frankfurt Richard L. Franklin Michael Frede Gottlob Frege Peter Geach Edmund Gettier Carl Ginet Alvin Goldman Gorgias Nicholas St. John Green H.Paul Grice Ian Hacking Ishtiyaque Haji Stuart Hampshire W.F.R.Hardie Sam Harris William Hasker R.M.Hare Georg W.F. Hegel Martin Heidegger Heraclitus R.E.Hobart Thomas Hobbes David Hodgson Shadsworth Hodgson Baron d'Holbach Ted Honderich Pamela Huby David Hume Ferenc Huoranszki William James Lord Kames Robert Kane Immanuel Kant Tomis Kapitan Walter Kaufmann Jaegwon Kim William King Hilary Kornblith Christine Korsgaard Saul Kripke Andrea Lavazza Christoph Lehner Keith Lehrer Gottfried Leibniz Jules Lequyer Leucippus Michael Levin George Henry Lewes C.I.Lewis David Lewis Peter Lipton C. Lloyd Morgan John Locke Michael Lockwood E. Jonathan Lowe John R. Lucas Lucretius Alasdair MacIntyre Ruth Barcan Marcus James Martineau Storrs McCall Hugh McCann Colin McGinn Michael McKenna Brian McLaughlin John McTaggart Paul E. Meehl Uwe Meixner Alfred Mele Trenton Merricks John Stuart Mill Dickinson Miller G.E.Moore Thomas Nagel Otto Neurath Friedrich Nietzsche John Norton P.H.Nowell-Smith Robert Nozick William of Ockham Timothy O'Connor Parmenides David F. Pears Charles Sanders Peirce Derk Pereboom Steven Pinker Plato Karl Popper Porphyry Huw Price H.A.Prichard Protagoras Hilary Putnam Willard van Orman Quine Frank Ramsey Ayn Rand Michael Rea Thomas Reid Charles Renouvier Nicholas Rescher C.W.Rietdijk Richard Rorty Josiah Royce Bertrand Russell Paul Russell Gilbert Ryle Jean-Paul Sartre Kenneth Sayre T.M.Scanlon Moritz Schlick Arthur Schopenhauer John Searle Wilfrid Sellars Alan Sidelle Ted Sider Henry Sidgwick Walter Sinnott-Armstrong J.J.C.Smart Saul Smilansky Michael Smith Baruch Spinoza L. Susan Stebbing Isabelle Stengers George F. Stout Galen Strawson Peter Strawson Eleonore Stump Francisco Suárez Richard Taylor Kevin Timpe Mark Twain Peter Unger Peter van Inwagen Manuel Vargas John Venn Kadri Vihvelin Voltaire G.H. von Wright David Foster Wallace R. Jay Wallace W.G.Ward Ted Warfield Roy Weatherford C.F. von Weizsäcker William Whewell Alfred North Whitehead David Widerker David Wiggins Bernard Williams Timothy Williamson Ludwig Wittgenstein Susan Wolf Scientists Michael Arbib Walter Baade Bernard Baars Leslie Ballentine Gregory Bateson John S. Bell Mara Beller Charles Bennett Ludwig von Bertalanffy Susan Blackmore Margaret Boden David Bohm Niels Bohr Ludwig Boltzmann Emile Borel Max Born Satyendra Nath Bose Walther Bothe Hans Briegel Leon Brillouin Stephen Brush Henry Thomas Buckle S. H. Burbury Donald Campbell Anthony Cashmore Eric Chaisson Gregory Chaitin Jean-Pierre Changeux Arthur Holly Compton John Conway John Cramer Francis Crick E. P. Culverwell Olivier Darrigol Charles Darwin Richard Dawkins Terrence Deacon Lüder Deecke Richard Dedekind Louis de Broglie Max Delbrück Abraham de Moivre Paul Dirac Hans Driesch John Eccles Arthur Stanley Eddington Gerald Edelman Paul Ehrenfest Albert Einstein Hugh Everett, III Franz Exner Richard Feynman R. A. Fisher Joseph Fourier Philipp Frank Steven Frautschi Edward Fredkin Lila Gatlin Michael Gazzaniga GianCarlo Ghirardi J. Willard Gibbs Nicolas Gisin Paul Glimcher Thomas Gold A. O. Gomes Brian Goodwin Joshua Greene Jacques Hadamard Mark Hadley Patrick Haggard Stuart Hameroff Augustin Hamon Sam Harris Hyman Hartman John-Dylan Haynes Donald Hebb Martin Heisenberg Werner Heisenberg John Herschel Art Hobson Jesper Hoffmeyer E. T. Jaynes William Stanley Jevons Roman Jakobson Pascual Jordan Ruth E. Kastner Stuart Kauffman Martin J. Klein William R. Klemm Christof Koch Simon Kochen Hans Kornhuber Stephen Kosslyn Ladislav Kovàč Leopold Kronecker Rolf Landauer Alfred Landé Pierre-Simon Laplace David Layzer Benjamin Libet Seth Lloyd Hendrik Lorentz Josef Loschmidt Ernst Mach Donald MacKay Henry Margenau James Clerk Maxwell Ernst Mayr John McCarthy Warren McCulloch Ulrich Mohrhoff Jacques Monod Emmy Noether Abraham Pais Howard Pattee Wolfgang Pauli Massimo Pauri Roger Penrose Steven Pinker Colin Pittendrigh Max Planck Susan Pockett Henri Poincaré Daniel Pollen Ilya Prigogine Hans Primas Adolphe Quételet Jürgen Renn/a> Juan Roederer Jerome Rothstein David Ruelle Tilman Sauer Jürgen Schmidhuber Erwin Schrödinger Aaron Schurger Claude Shannon David Shiang Herbert Simon Dean Keith Simonton B. F. Skinner Lee Smolin Ray Solomonoff Roger Sperry John Stachel Henry Stapp Tom Stonier Antoine Suarez Leo Szilard Max Tegmark William Thomson (Kelvin) Giulio Tononi Peter Tse Vlatko Vedral Heinz von Foerster John von Neumann John B. Watson Daniel Wegner Steven Weinberg Paul A. Weiss John Wheeler Wilhelm Wien Norbert Wiener Eugene Wigner E. O. Wilson Stephen Wolfram H. Dieter Zeh Ernst Zermelo Wojciech Zurek Konrad Zuse Fritz Zwicky Presentations Biosemiotics Free Will Mental Causation James Symposium |
E. T. Jaynes
Edwin Thompson Jaynes extended statistical mechanics to connect it to probability theory, Claude Shannon's information theory, and Bayesian statistical inferences.
Normal | Teacher | Scholar
He championed the work of J. Willard Gibbs, contrasting it to the earlier work of Ludwig Boltzmann. His 1957 "principle of maximum entropy" says that the probability distribution that best represents the current state of knowledge is the one with largest entropy. In 1964, Jaynes examined the difference between the Boltzmann and Gibbs formulations of the entropy. They differ, he says, because of different treatments of "interparticle forces." The status of the Gibbs and Boltzmann expressions for entropy has been a matter of some confusion in the literature. We show that:Jaynes explains that Gibbs entropy is a conserved quantity, for the same reason as the Louiville theorem that conserves the hyper-volume in phase space of a cloud of particles as it traverses its trajectory.
Boltzmann entropy increases. We can show that this is a consequence of quantal interactions during particle collisions, which deny the claim of microscopic irreversibility and erase the path information in the gas particles that would be needed to support Loschmidt's objection to the Boltzmann In the writer's 1962 Brandeis lectures on statistical mechanics, the Gibbs and Boltzmann expressions for entropy were compared briefly, and it was stated that the Gibbs formula gives the correct entropy, as defined in phenomenological thermodynamics, while the Boltzmann According to Jaynes (and Gibbs), information is conserved when macroscopic order disappears because it simply changes into microscopic (thus invisible) order as the path information of all the gas particles is preserved. As Boltzmann's mentor Joseph Loschmidt had argued in the early 1870's, if the velocities of all the particles could be reversed at an instant, the future evolution of the gas would move in the direction of decreasing entropy. All the original order would reappear. This is consistent with the idea of Pierre-Simon Laplace's super-intelligent demon and completely deterministic laws of nature. It also follows from the Louville theorem that the hyper-volume of a cloud of points in phase space is a constant as the system evolves. Classical mechanics and physical determinism was shown to be only an approximation for large numbers of particles shortly after Gibbs's death by Albert Einstein and the later "founders" of quantum mechanics. When quantum effects are included in the collision of gas particles, Boltzmann's idea of "molecular disorder" is seen to be correct and path information is destroyed. Nevertheless, Gibbs's idea of the conservation of information is still widely held today by mathematical physicists. And most texts on statistical mechanics still claim that microscopic collisions between particles are reversible. Some explicitly claim that quantum mechanics changes nothing, but that is because they limit themselves to the unitary (conservative and deterministic) evolution of the Schrödinger equation and ignore the collapse of the wave function.
For example, Richard Tolman (p.8) claimed that the “principle of dynamical reversibility” holds also in quantum mechanics in appropriate form, indicating that quantum theory supplies no new kind of element for understanding the actual irreversibility in the macroscopic behavior of physical systems. And D. ter Haar (p. 292) said “The transition from classical to statistical mechanics does not introduce any fundamental changes.”
This is because both classical and quantum statistical mechanics describe The origin of irreversibility depends on the ontological chance involved in von Neumann's Process 1, Dirac's projection postulate, the "collapse of the wave function," denied by so many interpretations of quantum mechanics and ignored in statistical mechanics texts. In her 2008 book, Carolyne Van Vliet (p.678) says that the theory of non-equilibrium statistical mechanics is incomplete without some kind of randomization at the microscopic level.
Ter Haar, D. 1995. Microscopic physics is irreversible as a consequence of ontological indeterminacy. Jaynes likely did not accept the collapse of the quantum mechanical wave function. He was strongly influenced by Eugene Wigner, who was an early denier of the projection postulate and supporter of the unitary evolution of the universal wave function. He says
I have profited from discussions of these problems, over many years, with Professor E. P. Wigner, from whom I first heard the remark, "Entropy is an anthropomorphic concept." Jaynes' view (and Gibbs') is philosophical determinism, for which information about the universe at one time gives us the information at all times (Laplace's demon). Boltzmann, like Maxwell before him (and Exner and Schrödinger after him - at least initially) knew that determinism cannot be proven by any experimental results. Jaynes is correct that statistical mechanics is a "branch of information theory."
References
Gibbs vs Boltzmann Entropies,
The Gibbs Paradox, in |