5 found
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  1. Time in Thermodynamics.Newton C. A. Da Costa & Adonai S. Sant'Anna - 2002 - Foundations of Physics 32 (11):1785-1796.
    We use Padoa's principle of independence of primitive symbols in axiomatic systems in order to show that time is dispensable in continuum thermodynamics, according to the axiomatic formulation of Gurtin and Williams. We also show how to define time by means of the remaining primitive concepts of Gurtin and Williams system. Finally, we introduce thermodynamics without time as a primitive concept.
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  2.  94
    Quasi-Set-Theoretical Foundations of Statistical Mechanics: A Research Program. [REVIEW]Adonai S. Sant'Anna & Alexandre M. S. Santos - 2000 - Foundations of Physics 30 (1):101-120.
    Quasi-set theory provides us a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the usual statistics (Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac) into the scope of quasi-set theory. We also show that, in order to derive Maxwell–Boltzmann statistics, it is not necessary to assume that the particles are distinguishable or individuals. In other words, Maxwell–Boltzmann statistics is possible even in an ensamble of indistinguishable particles, at least from the theoretical point of view. (...)
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  3.  63
    Elementary Particles, Hidden Variables, and Hidden Predicates.Adonai S. Sant'anna - 2000 - Synthese 125 (1-2):233 - 245.
    We recently showed that it is possible to deal withcollections of indistinguishable elementary particles (in thecontext of quantum mechanics) in a set-theoretical framework, byusing hidden variables. We propose in the presentpaper another axiomatics for collections of indiscernibleswithout hidden variables, where hidden predicates are implicitlyassumed. We also discuss the possibility of a quasi-settheoretical picture for quantum theory. Quasi-set theory, basedon Zermelo-Fraenkel set theory, was developed for dealing withcollections of indistinguishable, but, not identical objects.
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    Elementary Particles, Hidden Variables, And Hidden Predicates.Adonai S. Sant'anna - 2000 - Synthese 125 (1):233-245.
    We recently showed that it is possible to deal with collections of indistinguishable elementary particles in a set-theoretical framework, by using hidden variables. We propose in the present paper another axiomatics for collections of indiscernibles without hidden variables, where hidden predicates are implicitly assumed. We also discuss the possibility of a quasi-set theoretical picture for quantum theory. Quasi-set theory, based on Zermelo-Fraenkel set theory, was developed for dealing with collections of indistinguishable, but, not identical objects.
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  5. Individuality, Quasi-Sets and the Double-Slit Experiment.Adonai S. Sant'Anna - forthcoming - Quantum Studies: Mathematics and Foundations.
    Quasi-set theory $\cal Q$ allows us to cope with certain collections of objects where the usual notion of identity is not applicable, in the sense that $x = x$ is not a formula, if $x$ is an arbitrary term. $\cal Q$ was partially motivated by the problem of non-individuality in quantum mechanics. In this paper I discuss the range of explanatory power of $\cal Q$ for quantum phenomena which demand some notion of indistinguishability among quantum objects. My main focus is (...)
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