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  1. Quantum Time Arrows, Semigroups and Time-Reversal in Scattering.Robert C. Bishop - 2005 - International Journal of Theoretical Physics:723-733.
    Two approaches toward the arrow of time for scattering processes have been proposed in rigged Hilbert space quantum mechanics. One, due to Arno Bohm, involves preparations and registrations in laboratory operations and results in two semigroups oriented in the forward direction of time. The other, employed by the Brussels-Austin group, is more general, involving excitations and de-excitations of systems, and apparently results in two semigroups oriented in opposite directions of time. It turns out that these two time arrows can be (...)
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  2. Arrow of Time in Rigged Hilbert Space Quantum Mechanics.Robert C. Bishop - 2004 - International Journal of Theoretical Physics 43 (7):1675–1687.
    Arno Bohm and Ilya Prigogine's Brussels-Austin Group have been working on the quantum mechanical arrow of time and irreversibility in rigged Hilbert space quantum mechanics. A crucial notion in Bohm's approach is the so-called preparation/registration arrow. An analysis of this arrow and its role in Bohm's theory of scattering is given. Similarly, the Brussels-Austin Group uses an excitation/de-excitation arrow for ordering events, which is also analyzed. The relationship between the two approaches is discussed focusing on their semi-group operators and time (...)
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  3. Correlations Without Joint Distributions in Quantum Mechanics.Nancy Cartwright - 1974 - Foundations of Physics 4 (1):127-136.
    The use of joint distribution functions for noncommuting observables in quantum thermodynamics is investigated in the light of L. Cohen's proof that such distributions are not determined by the quantum state. Cohen's proof is irrelevant to uses of the functions that do not depend on interpreting them as distributions. An example of this, from quantum Onsager theory, is discussed. Other uses presuppose that correlations betweenp andq values depend at least on the state. But correlations may be fixed by the state (...)
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  4. Entanglement and Thermodynamics in General Probabilistic Theories.Giulio Chiribella & Carlo Maria Scandolo - 2015 - New Journal of Physics 17:103027.
    Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum. More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification between entropies and measures of pure state entanglement. Here we search for the roots of this connection, investigating the relation between entanglement and thermodynamics in the framework of general probabilistic theories. We first address the question whether an entangled state can be transformed into another by (...)
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  5. Operational Axioms for Diagonalizing States.Giulio Chiribella & Carlo Maria Scandolo - 2015 - EPTCS 195:96-115.
    In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and quantum statistical mechanics, where it provides the foundation for the notions of majorization and entropy. A natural question then arises: can we reconstruct these notions from purely operational axioms? We address this question in the framework of general probabilistic theories, presenting a set of axioms that guarantee that (...)
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  6. Connections Between the Thermodynamics of Classical Electrodynamic Systems and Quantum Mechanical Systems for Quasielectrostatic Operations.Daniel C. Cole - 1999 - Foundations of Physics 29 (12):1819-1847.
    The thermodynamic behavior is analyzed of a single classical charged particle in thermal equilibrium with classical electromagnetic thermal radiation, while electrostatically bound by a fixed charge distribution of opposite sign. A quasistatic displacement of this system in an applied electrostatic potential is investigated. Treating the system nonrelativistically, the change in internal energy, the work done, and the change in caloric entropy are all shown to be expressible in terms of averages involving the distribution of the position coordinates alone. A convenient (...)
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  7. How to ‘See Through’ the Ideal Gas Law in Terms of the Concepts of Quantum Mechanics.Malcolm R. Forster & Alexei Krioukov - unknown
    Textbooks in quantum mechanics frequently claim that quantum mechanics explains the success of classical mechanics because “the mean values [of quantum mechanical observables] follow the classical equations of motion to a good approximation,” while “the dimensions of the wave packet be small with respect to the characteristic dimensions of the problem.” The equations in question are Ehrenfest’s famous equations. We examine this case for the one-dimensional motion of a particle in a box, and extend the idea deriving a special case (...)
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  8. The Emergence of the Macroworld: A Study of Intertheory Relations in Classical and Quantum Mechanics.Malcolm R. Forster & Alexey Kryukov - 2003 - Philosophy of Science 70 (5):1039-1051.
    Classical mechanics is empirically successful because the probabilistic mean values of quantum mechanical observables follow the classical equations of motion to a good approximation (Messiah 1970, 215). We examine this claim for the one-dimensional motion of a particle in a box, and extend the idea by deriving a special case of the ideal gas law in terms of the mean value of a generalized force used to define "pressure." The examples illustrate the importance of probabilistic averaging as a method of (...)
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  9. Bohmian Mechanics and Quantum Equilibrium.Sheldon Goldstein, D. Dürr & N. Zanghì - manuscript
    in Stochastic Processes, Physics and Geometry II, edited by S. Albeverio, U. Cattaneo, D. Merlini (World Scientific, Singapore, 1995) pp. 221-232.
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  10. On the Uniqueness of Quantum Equilibrium in Bohmian Mechanics.Sheldon Goldstein & W. Struyve - manuscript
    In Bohmian mechanics the distribution |ψ|2 is regarded as the equilibrium distribution. We consider its uniqueness, finding that it is the unique equivariant distribution that is also a local functional of the wave function ψ.
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  11. Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John Von Neumann's 1929 Article on the Quantum Ergodic Theorem.Sheldon Goldstein & Roderich Tumulka - unknown
    The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann’s 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to be much misunderstood. In it, von Neumann studied the long-time behavior of macroscopic quantum systems. While one of the two theorems announced in his title, the one he calls the (...)
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  12. Normal Typicality and Von Neumann's Quantum Ergodic Theorem.Sheldon Goldstein & Roderich Tumulka - unknown
    We discuss the content and significance of John von Neumann’s quantum ergodic theorem (QET) of 1929, a strong result arising from the mere mathematical structure of quantum mechanics. The QET is a precise formulation of what we call normal typicality, i.e., the statement that, for typical large systems, every initial wave function ψ0 from an energy shell is “normal”: it evolves in such a way that |ψt ψt| is, for most t, macroscopically equivalent to the micro-canonical density matrix. The QET (...)
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  13. On the Approach to Thermal Equilibrium of Macroscopic Quantum Systems.Sheldon Goldstein & Roderich Tumulka - unknown
    We consider an isolated, macroscopic quantum system. Let H be a microcanonical “energy shell,” i.e., a subspace of the system’s Hilbert space spanned by the (finitely) many energy eigenstates with energies between E and E + δE. The thermal equilibrium macro-state at energy E corresponds to a subspace Heq of H such that dim Heq/ dim H is close to 1. We say that a system with state vector ψ H is in thermal equilibrium if ψ is “close” to Heq. (...)
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  14. Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann’s 1929 Article on the Quantum Ergodic Theorem.Sheldon Goldstein, Roderich Tumulka, Joel L. Lebowitz & Nino Zangh`ı - unknown
    The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann’s 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to be much misunderstood. In it, von Neumann studied the long-time behavior of macroscopic quantum systems. While one of the two theorems announced in his title, the one he calls the (...)
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  15. A Formulation of Quantum Stochastic Processes and Some of its Properties.K. -E. Hellwig & W. Stulpe - 1983 - Foundations of Physics 13 (7):673-699.
    In an earlier paper by one of us [K.-E. Hellwig (1981)], elements of discrete quantum stochastic processes which arise when the classical probability space is replaced by quantum theory have been considered. In the present paper a general formulation is given and its properties are compared with those of classical stochastic processes. Especially, it is asked whether such processes can be Markovian. An example is given and similarities to methods in quantum statistical thermodynamics are pointed out.
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  16. Thermal Equilibrium Between Radiation and Matter.G. Lanyi - 2003 - Foundations of Physics 33 (3):511-528.
    In 1916, Einstein rederived the blackbody radiation law of Planck that originated the idea of quantized energy one hundred years ago. For this purpose, Einstein introduced the concept of transition probability, which had a profound influence on the development of quantum theory. In this article, we adopt Einstein's assumptions with two exceptions and seek the statistical condition for the thermal equilibrium of matter without referring to the inner details of either statistical thermodynamics or quantum theory. It is shown that the (...)
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  17. Is “Relative Quantum Phase” Transitive?A. J. Leggett - 1995 - Foundations of Physics 25 (1):113-122.
    I discuss the question: Is it possible to prepare, by purely thermodynamic means, an ensemble described by a quantum state having a definite phase relation between two component states which have never been in direct contact? Resolution of this question requires us to take explicit account of the nature of the correlations between the system and its thermal environment.
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  18. Quantum Statistical Dynamics: Statistics Origin, Measurement, and Irreversibility. [REVIEW]V. S. Mashkevich - 1985 - Foundations of Physics 15 (1):1-33.
    It is shown that in the quantum theory of systems with a finite number of degrees of freedom which employs a set of algebraic states, a statistical element introduced by averaging the mean values of operators over the distribution of continuous quantities (a spectrum point of a canonical operator and time) is conserved for the limiting transition to the δ distribution. On that basis, quantum statistical dynamics, i.e., a theory in which dynamics (time evolution) includes a statistical element, is advanced. (...)
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  19. On Transformations of Physical Systems.L. S. Mayants - 1976 - Foundations of Physics 6 (5):485-510.
    A universal, unified theory of transformations of physical systems based on the propositions of probabilistic physics is developed. This is applied to the treatment of decay processes and intramolecular rearrangements. Some general features of decay processes are elucidated. A critical analysis of the conventional quantum theories of decay and of Slater's quantum theory of intramolecular rearrangements is given. It is explained why, despite the incorrectness of the decay theories in principle, they can give correct estimations of decay rate constants. The (...)
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  20. Quantum Statistical Mechanics as a Construction of an Embedding Scheme.Olaf Melsheimer - 1983 - Foundations of Physics 13 (7):745-758.
    The aim of the present paper is to show that the formalism of equilibrium quantum statistical mechanics can fully be incorporated into Ludwig's embedding scheme for classical theories in many-body quantum mechanics. A construction procedure based on a recently developed reconstruction procedure for the so-called macro-observable is presented which leads to the explicit determination of the set of classical ensembles compatible with the embedding scheme.
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  21. The Formalism of Equilibrium Quantum Statistical Mechanics Revisited.Olaf Melsheimer - 1982 - Foundations of Physics 12 (1):59-84.
    It is shown that the traditional formalism of equilibrium quantum statistical mechanics may fully be incorporated into a general macro-observable approach to quantum statistical mechanics recently proposed by the same author. (1,2) In particular, the partition functions which in the traditional approach are assumed to connect nonnormalized density operators with thermodynamic functions are reinterpreted as functions connecting so-called quantum mechanical effect operators with state parameters. It is argued that these functions although only part of a much richer internal structure of (...)
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  22. On the Classical Content of Many-Body Quantum Mechanics.Olaf Melsheimer - 1979 - Foundations of Physics 9 (3-4):193-215.
    The aim of this paper is to reconcile the two modes of description of macrosystems, i.e., to remove certain inconsistencies between the classical phenomenological and the quantum-theoretical descriptions of a macrosystem. Starting from Ludwig's formulation of a general framework for classical theories and his ansatz for a compatibility condition between the quantum theoretical and the classical mode of description for a macrosystem, we try to make clear what the “classical content” of many-body quantum theory really is. It is shown that (...)
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  23. Einstein’s Miraculous Argument of 1905: The Thermodynamic Grounding of Light Quanta.John D. Norton - manuscript
    A major part of Einstein’s 1905 light quantum paper is devoted to arguing that high frequency heat radiation bears the characteristic signature of a microscopic energy distribution of independent, spatially localized components. The content of his light quantum proposal was precarious in that it contradicted the great achievement of nineteenth century physics, the wave theory of light and its accommodation in electrodynamics. However the methods used to arrive at it were both secure and familiar to Einstein in 1905. A mainstay (...)
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  24. Atoms, Entropy, Quanta: Einstein’s Miraculous Argument of 1905.John D. Norton - 2005 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 37 (1):71-100.
    In the sixth section of his light quantum paper of 1905, Einstein presented the miraculous argument, as I shall call it. Pointing out an analogy with ideal gases and dilute solutions, he showed that the macroscopic, thermodynamic properties of high frequency heat radiation carry a distinctive signature of finitely many, spatially localized, independent components and so inferred that it consists of quanta. I describe how Einstein’s other statistical papers of 1905 had already developed and exploited the idea that the ideal (...)
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  25. Quantum-Mechanical Statistics and the Inclusivist Approach to the Nature of Particulars.Francesco Orilia - 2006 - Synthese 148 (1):57-77.
    There have been attempts to derive anti-haeccetistic conclusions from the fact that quantum mechanics (QM) appeals to non-standard statistics. Since in fact QM acknowledges two kinds of such statistics, Bose-Einstein and Fermi-Dirac, I argue that we could in the same vein derive the sharper anti-haeccetistic conclusion that bosons are bundles of tropes and fermions are bundles of universals. Moreover, since standard statistics is still appropriate at the macrolevel, we could also venture to say that no anti-haecceitistic conclusion is warranted for (...)
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  26. Exact Quantum-Statistical Dynamics of Time-Dependent Generalized Oscillators.Don Page - manuscript
    Using linear invariant operators in a constructive way we find the most general thermal density operator and Wigner function for time-dependent generalized oscillators. The general Wigner function has five free parameters and describes the thermal Wigner function about a classical trajectory in phase space. The contour of the Wigner function depicts an elliptical orbit with a constant area moving about the classical trajectory, whose eccentricity determines the squeezing of the initial vacuum.
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  27. Generalized Jarzynski Equality.Don N. Page - unknown
    The Jarzynski equality equates the mean of the exponential of the negative of the work (per fixed temperature) done by a changing Hamiltonian on a system, initially in thermal equilibrium at that temperature, to the ratio of the final to the initial equilibrium partition functions of the system at that fixed temperature. It thus relates two thermal equilibrium quantum states.
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  28. Thermodynamic Aspects of Schrödinger's Probability Relations.James L. Park - 1988 - Foundations of Physics 18 (2):225-244.
    Using Schrödinger's generalized probability relations of quantum mechanics, it is possible to generate a canonical ensemble, the ensemble normally associated with thermodynamic equilibrium, by at least two methods, statistical mixing and subensemble selection, that do not involve thermodynamic equilibration. Thus the question arises as to whether an observer making measurements upon systems from a canonical ensemble can determine whether the systems were prepared by mixing, equilibration, or selection. Investigation of this issue exposes antinomies in quantum statistical thermodynamics. It is conjectured (...)
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  29. Generalized Two-Level Quantum Dynamics. III. Irreversible Conservative Motion.James L. Park & William Band - 1978 - Foundations of Physics 8 (3-4):239-254.
    If the ordinary quantal Liouville equation ℒρ= $\dot \rho $ is generalized by discarding the customary stricture that ℒ be of the standard Hamiltonian commutator form, the new quantum dynamics that emerges has sufficient theoretical fertility to permit description even of a thermodynamically irreversible process in an isolated system, i.e., a motion ρ(t) in which entropy increases but energy is conserved. For a two-level quantum system, the complete family of time-independent linear superoperators ℒ that generate such motions is derived; and (...)
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  30. Generalized Two-Level Quantum Dynamics. I. Representations of the Kossakowski Conditions.James L. Park & William Band - 1977 - Foundations of Physics 7 (11-12):813-825.
    This communication is part I of a series of papers which explore the theoretical possibility of generalizing quantum dynamics in such a way that the predicted motions of an isolated system would include the irreversible (entropy-increasing) state evolutions that seem essential if the second law of thermodynamics is ever to become a theorem of mechanics. In this first paper, the general mathematical framework for describing linear but not necessarily Hamiltonian mappings of the statistical operator is reviewed, with particular attention to (...)
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  31. Rigorous Information-Theoretic Derivation of Quantum-Statistical Thermodynamics. I.James L. Park & William Band - 1977 - Foundations of Physics 7 (3-4):233-244.
    In previous publications we have criticized the usual application of information theory to quantal situations and proposed a new version of information-theoretic quantum statistics. This paper is the first in a two-part series in which our new approach is applied to the fundamental problem of thermodynamic equilibrium. Part I deals in particular with informational definitions of equilibrium and the identification of thermodynamic analogs in our modified quantum statistics formalism.
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  32. Quasi-Probability Distributions for Arbitrary Spin-J Particles.G. Ramachandran, A. R. Usha Devi, P. Devi & Swarnamala Sirsi - 1996 - Foundations of Physics 26 (3):401-412.
    Quasi-probability distribution functions fj WW, fj MM for quantum spin-j systems are derived based on the Wigner-Weyl, Margenau-Hill approaches. A probability distribution fj sph which is nonzero only on the surface of the sphere of radius √j(j+1) is obtained by expressing the characteristic function in terms of the spherical moments. It is shown that the Wigner-Weyl distribution function turns out to be a distribution over the sphere in the classical limit.
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  33. A Matter of Degree: Putting Unitary Inequivalence to Work.Laura Ruetsche - 2002 - Philosophy of Science 70 (5):1329-1342.
    If a classical system has infinitely many degrees of freedom, its Hamiltonian quantization need not be unique up to unitary equivalence. I sketch different approaches (Hilbert space and algebraic) to understanding the content of quantum theories in light of this non‐uniqueness, and suggest that neither approach suffices to support explanatory aspirations encountered in the thermodynamic limit of quantum statistical mechanics.
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  34. Covariant Relativistic Statistical Mechanics of Many Particles.Wm C. Schieve - 2005 - Foundations of Physics 35 (8):1359-1381.
    In this paper the quantum covariant relativistic dynamics of many bodies is reconsidered. It is emphasized that this is an event dynamics. The events are quantum statistically correlated by the global parameter τ. The derivation of an event Boltzmann equation emphasizes this. It is shown that this Boltzmann equation may be viewed as exact in a dilute event limit ignoring three event correlations. A quantum entropy principle is obtained for the marginal Wigner distribution function. By means of event linking (concatenations) (...)
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  35. The Transitions Among Classical Mechanics, Quantum Mechanics, and Stochastic Quantum Mechanics.Franklin E. Schroeck Jr - 1982 - Foundations of Physics 12 (9):825-841.
    Various formalisms for recasting quantum mechanics in the framework of classical mechanics on phase space are reviewed and compared. Recent results in stochastic quantum mechanics are shown to avoid the difficulties encountered by the earlier approach of Wigner, as well as to avoid the well-known incompatibilities of relativity and ordinary quantum theory. Specific mappings among the various formalisms are given.
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  36. Is - Ktr(Ln) the Entropy in Quantum Mechanics.Orly Shenker - 1999 - British Journal for the Philosophy of Science 50 (1):33-48.
    In quantum mechanics, the expression for entropy is usually taken to be -kTr(ln), where is the density matrix. The convention first appears in Von Neumann's Mathematical Foundations of Quantum Mechanics. The argument given there to justify this convention is the only one hitherto offered. All the arguments in the field refer to it at one point or another. Here this argument is shown to be invalid. Moreover, it is shown that, if entropy is -kTr(ln), then perpetual motion machines are possible. (...)
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  37. Stochastic Dynamics of Quantum-Mechanical Systems.E. C. G. Sudarshan, P. M. Mathews & Jayaseetha Rau - 1961 - Physical Review 121:920--924.
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  38. Quantum State Diffusion - Ian Percival, Quantum State Diffusion, Cambridge University Press, Cambridge, 1998. [REVIEW]P. T. - 2002 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 33 (4):707-716.
  39. On the Time Scales in the Approach to Equilibrium of Macroscopic Quantum Systems.Hal Tasaki, Sheldon Goldstein & Takashi Hara - unknown
    The recent renewed interest in the foundation of quantum statistical mechanics and in the dynamics of isolated quantum systems has led to a revival of the old approach by von Neumann to investigate the problem of thermalization only in terms of quantum dynamics in an isolated system [1, 2]. It has been demonstrated in some general or concrete settings that a pure initial state evolving under quantum dynamics indeed approaches an equilibrium state [3–9]. The underlying idea that a single pure (...)
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