Ruelle: Thermodynamic Formalism

Zitat

„Outside of statistical mechanics proper, the thermodynamic formalism and its mathematical methods have now been used extensively in constructive quantum field theory and in the study of certain differentiable dynamical systems (notably Anosov diffeomorphisms and flows).“ (p. 1) #Ruelle #thermodynamic #formalism

Ruelle, David, Thermodynamic Formalism. The Mathematical Structures of Equilibrium. Statistical Mechanics. Cambridge, UK: Cambridge University Press 22004.

Ruelle: The states of classical systems

Zitat

„For classical systems the states are probability measures on an appropriate space of infinite configurations; such states can also be viewed as linear functionals on an abelian algebra (an algebra of continuous functions in the case of Radon measures).“ (p. 2) #Ruelle #system #states

Ruelle, David, Thermodynamic Formalism. The Mathematical Structures of Equilibrium. Statistical Mechanics. Cambridge, UK: Cambridge University Press 22004.

Brunschvicq: La physique mathématique

Zitat

„La physique mathématique s’est développée sous deux formes différentes qui avaient mis aux prises, d’abord l’école française de Descartes et l’école italienne de Galilée et de Torricelli, puis les partisans de Leibniz et les partisans de Newton : les uns, géomètres purs qui procédaient par déduction a priori, les autres, observateurs avant tout, qui prétendaient ne relever que de l’expérience.“ (p. 253) #Brunschvicq #Descartes #Galilée #Torricelli #Leibniz #Newton #physique #mathématique

Brunschvicg, Léon, Les étapes de la philosophie mathématique. Paris: Alcan 1912. 658 S.

Ruelle: Phase Transition

Zitat

„The main physical problem which equilibrium statistical mechanics tries to clarify is that of phase transitions. When the temperature of water is lowered, why do its properties change first smoothly, then suddenly as the freezing point is reached?“ (p. 1) #Ruelle #PhaseTransition

Ruelle, David, Thermodynamic Formalism. The Mathematical Structures of Equilibrium. Statistical Mechanics. Cambridge, UK: Cambridge University Press 22004.

Yourgrau: The Complete Set of Mathematical Truths

Zitat

„The complete set of mathematical truths will never be captured by any finite or recursive list of axioms that is fully formal. Thus, no mechanical device, no computer, will ever be able to exhaust the truths of mathematics. It follows immediately, as Gödel was quick to point out, that if we are able somehow to grasp the complete truth in this domain, then we, or our minds, are not machines or computers. (Enthusiasts of artificial intelligence were not amused.)“ (p. 3) #Yourgrau #Gödel #MathematicalTruth

Yourgrau, Palle, A World Without Time. The Forgotten Legacy of Gödel and Einstein. New York: Basic Books 2005.