4 found
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  1.  78
    Classical Distinguishability and the Gibbs-Liouville Theorem.Andreas Henriksson - manuscript
    It is shown that the theory of classical mechanics can be built from the concept of distinguishability between pairs of classical states. The non-ignorant observer can, with infinite precision, distinguish between arbitrary pairs. Either they are identical, or they are distinct. The distinguishability is postulated to be conserved in time for closed systems. The mathematical representation of this postulate is shown to be given by the Gibbs-Liouville theorem. Alternative statements of this theorem are given. In particular, Hamilton's principle is derived (...)
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  2.  41
    On the Second Law of Thermodynamics.Andreas Henriksson - manuscript
    In this article, it is argued that, given an initial uncertainty in the state of a system, the information possessed about the system, by any given observer, tend to decrease exponentially until there is none left. By linking the subjective, i.e. observer dependent, concepts of information and entropy, the statement of information decrease represent an alternative formulation of the second law of thermodynamics. With this reformulation, the connection between the foundations of statistical mechanics and classical mechanics is clarified. In conclusion, (...)
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  3.  37
    Fidelity and Mistaken Identity for Symplectic Quantum States.Andreas Henriksson - manuscript
    The distinguishability between pairs of quantum states, as measured by quantum fidelity, is formulated on phase space. The fidelity is physically interpreted as the probability that the pair are mistaken for each other upon an measurement. The mathematical representation is based on the concept of symplectic capacity in symplectic topology. The fidelity is the absolute square of the complex-valued overlap between the symplectic capacities of the pair of states. The symplectic capacity for a given state, onto any conjugate plane of (...)
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  4.  16
    Quantum Superpositions and the Measurement Problem.Andreas Henriksson - manuscript
    The measurement problem is addressed from the viewpoint that it is the distinguishability between the state preparation and its quantum ensemble, i.e. the set of states with which it has a non-zero overlap, that is at the heart of the difference between classical and quantum measurements. The measure for the degree of distinguishability between pairs of quantum states, i.e. the quantum fidelity, is for this purpose generalized, by the application of the superposition principle, to the setting where there exists an (...)
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