scholarly journals Phenomenological quantum thermodynamics resource theory for closed bipartite Schottky systems

2020 ◽  
Vol 378 (2170) ◽  
pp. 20190173 ◽  
Author(s):  
Wolfgang Muschik
Keyword(s):  
Quantum Mechanics ◽  
Density Operator ◽  
Nonequilibrium Thermodynamics ◽  
Discrete Systems ◽  
Resource Theory ◽  
Quantum Thermodynamics ◽  
Theme Issue ◽  
Von Neumann ◽  
Starting Point ◽  
Von Neumann Equation

How to introduce thermodynamics to quantum mechanics? From numerous possibilities of solving this task, the simple choice is here: the conventional von Neumann equation deals with a density operator whose probability weights are time-independent. Because there is no reason apart from the reversible quantum mechanics that these weights have to be time-independent, this constraint is waived, which allows one to introduce thermodynamical concepts to quantum mechanics. This procedure is similar to that of Lindblad’s equation, but different in principle. But beyond this simple starting point, the applied thermodynamical concepts of discrete systems may perform a ‘source theory’ for other versions of phenomenological quantum thermodynamics. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

scholarly journals Concepts of Phenomenological Irreversible Quantum Thermodynamics I: Closed Undecomposed Schottky Systems in Semi-Classical Description

2019 ◽  
Vol 44 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Wolfgang Muschik
Keyword(s):  
Time Dependent ◽  
Quantum Thermodynamics ◽  
Time Rate ◽  
Von Neumann ◽  
Classical Description ◽  
Von Neumann Equation

Abstract If the von Neumann equation is modified by time dependent statistical weights, the time rate of entropy, the entropy exchange and the production of a Schottky system are derived whose Hamiltonian does not contain the interaction with the system’s environment. This interaction is semi-classically described by the quantum theoretical expressions of power and entropy exchange.

Verallgemeinerte physikalische Entropien auf informationstheoretischer Grundlage

1965 ◽  
Vol 20 (12) ◽  
pp. 1543-1553 ◽  
Author(s):  
H. Schwegler
Keyword(s):  
Density Operator ◽  
Gibbs Equation ◽  
Macroscopic Equation ◽  
Von Neumann ◽  
Special Cases ◽  
Self Consistent ◽  
Von Neumann Equation ◽  
The Times ◽  
Experimental Values ◽  
Special Case

Physical entropies SB are defined with respect to a certain set of variables, the observationlevel B. For all times in which B exists, SB is the uncertainty H of a density operator RB making H a maximum with respect to the experimental values of B. This definition is not restricted to the thermodynamic equilibrium. The entropies SB measure the vagueness of the description in Hilbert-space caused by the choice of B. The time dependence of the density operator RB is not governed by the von Neumann equation, but in the special case of a “self-consistent“ B it may be calculated with the help of this equation. An increasing SB is obtained.If the times for which B exists are sufficiently close, a macroscopic equation for the time deriva· tive of SB is given. Three special cases of B are considered, leading to the Gibbs equation, a generalized entropy equation for heat conduction and an entropy equation for the multipole relaxation.

DISSIPATIVE BLACKBODY RADIATION: RADIATION IN A LOSSY CAVITY

2004 ◽  
Vol 18 (03) ◽  
pp. 317-324 ◽  
Author(s):  
J. R. CHOI
Keyword(s):  
Energy Density ◽  
Density Operator ◽  
Invariant Operator ◽  
Blackbody Radiation ◽  
Von Neumann ◽  
The Media ◽  
Von Neumann Equation

We defined normalized density operator that satisfies Liouville–von Neumann equation in terms of the invariant operator. The energy density inside the cavity decreased exponentially with time due to the conductivity of the media. We also evaluated the total number of photons in the cavity.

GEODESIC FLOWS, VON NEUMANN EQUATION AND QUANTUM MECHANICS ON NONCOMMUTATIVE CYLINDER

2006 ◽  
Vol 21 (28) ◽  
pp. 2151-2160
Author(s):  
PARTHA GUHA
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Geodesic Flows ◽  
Von Neumann ◽  
Discrete Schrödinger Equation ◽  
Von Neumann Equation ◽  
Area Preserving

We study quantum mechanics on the noncommutative cylinder via Moyal deformed geodesic flows on the group of area preserving diffeomorphism. This equation coincides exactly with the von Neumann equation. Using discretization techniques of Kemmoku and Saito we obtain the discrete Schrödinger equation on noncommutative cylinder. Thus we reproduce the result of Balachandran et al.1

scholarly journals SYMPLECTIC STRUCTURES AND QUANTUM MECHANICS

1996 ◽  
Vol 10 (12) ◽  
pp. 545-553 ◽  
Author(s):  
GIUSEPPE MARMO ◽  
GAETANO VILASI
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Classical Field Theory ◽  
General Setting ◽  
Von Neumann ◽  
Neumann Theorem ◽  
Starting Point ◽  
Good Starting Point ◽  
Von Neumann Theorem

Canonical coordinates for the Schrödinger equation are introduced, making more transparent its Hamiltonian structure. It is shown that the Schrödinger equation, considered as a classical field theory, shares with Liouville completely integrable field theories the existence of a recursion operator which allows for the infinitely many conserved functionals pairwise commuting with respect to the corresponding Poisson bracket. The approach may provide a good starting point to get a clear interpretation of Quantum Mechanics in the general setting, provided by Stone–von Neumann theorem, of Symplectic Mechanics. It may give new tools to solve in the general case the inverse problem of quantum mechanics whose solution is given up to now only for one-dimensional systems by the Gel’fand-Levitan-Marchenko formula.

scholarly journals Resource theory of contextuality

2019 ◽  
Vol 377 (2157) ◽  
pp. 20190010
Author(s):  
Barbara Amaral
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Point Of View ◽  
Resource Theory ◽  
Quantum Property ◽  
Theme Issue ◽  
Formal Treatment ◽  
Recent Developments ◽  
Potential Resource

In addition to the important role of contextuality in foundations of quantum theory, this intrinsically quantum property has been identified as a potential resource for quantum advantage in different tasks. It is thus of fundamental importance to study contextuality from the point of view of resource theories, which provide a powerful framework for the formal treatment of a property as an operational resource. In this contribution, we review recent developments towards a resource theory of contextuality and connections with operational applications of this property. This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond’.

Quantum contextuality in the Copenhagen approach

2019 ◽  
Vol 377 (2157) ◽  
pp. 20190025 ◽  
Author(s):  
Gregg Jaeger
Keyword(s):  
Quantum Mechanics ◽  
Experimental Situation ◽  
Hidden Variables ◽  
Theme Issue ◽  
Standard Quantum ◽  
Von Neumann ◽  
Physical Description ◽  
Quantum Contextuality ◽  
Quantum Observables

The origin and basis of the notion of quantum contextuality is identified in the Copenhagen approach to quantum mechanics, where context is automatically invoked by its requirement that the experimental arrangement involved in any measurements or set of measurements be taken into account while, in general, the outcome of a measurement may depend on other measurements immediately preceding or jointly performed on the same system. For Bohr, the specification of the experimental situation of any measurement is essential to its significance in light of complementarity and the omnipresence of the quantum of action in physics; for Heisenberg, the incompatibility of pairs of sharp measurements belonging to different situations coheres with both the completeness of the quantum state as an objective physical description and the principle of indeterminacy. Here, context in the Copenhagen approach is taken to be the equivalence class of experimental arrangements corresponding to a set of compatible measurements of quantum observables in standard quantum mechanics; the associated form of contextuality in quantum mechanics arises via the non-commutativity in general of sharp observables, proven by von Neumann, that can appear, providing different contexts. This notion is related to theoretical situations explored later by Bell, by Kochen and Specker, and by others in relation to the classification of hidden-variables theories and elsewhere in physics. This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond’.

scholarly journals Contextuality, memory cost and non-classicality for sequential measurements

2019 ◽  
Vol 377 (2157) ◽  
pp. 20190141 ◽  
Author(s):  
Costantino Budroni
Keyword(s):  
Quantum Mechanics ◽  
Experimental Test ◽  
Quantum Systems ◽  
Theme Issue ◽  
Theoretical Frameworks ◽  
Temporal Correlations ◽  
Starting Point ◽  
Classical Correlations ◽  
Memory Cost ◽  
Sequential Measurements

The Kochen–Specker theorem, and the associated notion of quantum contextuality, can be considered as the starting point for the development of a notion of non-classical correlations for single systems. The subsequent debate around the possibility of an experimental test of Kochen–Specker-type contradiction stimulated the development of different theoretical frameworks to interpret experimental results. Starting from the approach based on sequential measurements, we will discuss a generalization of the notion of non-classical temporal correlations that goes beyond the contextuality approach and related ones based on Leggett and Garg's notion of macrorealism, and it is based on the notion of memory cost of generating correlations. Finally, we will review recent results on the memory cost for generating temporal correlations in classical and quantum systems. The present work is based on the talk given at the Purdue Winer Memorial Lectures 2018: probability and contextuality. This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond’.

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