Temperature Relaxation between Systems with Negative Kelvin Temperatures

Zylka, Ch.; Vojta, G.

doi:10.1515/zna-1987-0605

Zeitschrift Für Naturforschung A

1987

DOI: 10.1515/zna-1987-0605

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Temperature Relaxation between Systems with Negative Kelvin Temperatures

Ch. Zylka

G. Vojta

Abstract: We investigate the problem of distributing a given amount of heat among three systems under the following conditions: The systems are able to exhibit negative Kelvin temperatures, and heat equalization always fulfills a harmonic mixing rule+ T (2) ). Just this happens for spin systems in the high temperature approximation.

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1989

1991

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Cited by 3 publications

(1 citation statement)

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“…From the Wigner-Kirkwood series for the partition function, corresponding series expansions for the thermodynamic potentials follow in the well-known manner. A more detailed paper including the quantum statistics of relativistic anharmonic oscillators with singular potentials will be published elsewhere [27].…”

mentioning

confidence: 99%

Relativistic Quantum Statistics in the Wigner Formalism and its Applications to the Toda Oscillator

Hamo¹,

Vojta²,

Zylka³

1991

Europhys. Lett.

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The Wigner-Kirkwood series expansion of equilibrium quantum statistics in the phase space formalism is generalized to include relativistic systems. For partition functions and all thermodynamic functions the series yields quantum corrections in terms of powers of h2 including systematic relativistic corrections given by modified Hankel functions 9@nc2/kT). An application to the symmetric relativistic quantum Toda oscillator is sketched.

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mentioning

confidence: 99%

Relativistic Quantum Statistics in the Wigner Formalism and its Applications to the Toda Oscillator

Hamo¹,

Vojta²,

Zylka³

1991

Europhys. Lett.

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Über das monotone Verhalten gewisser Zustandssummen bei Temperaturausgleich

Zylka

1989

Annalen der Physik

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Prof, Dr. G. Vojtn zum 60. Ceburtstag zugeeignet I n h a l t s u b e r s i c h t . Wir lenken die Aufmerksamkeit darauf, daB die kanonische Zustnndsumme Z(/3', ,P, .. ., 8") = Z(p) eines aus n unabhangigen Teilsystemen zusammengesetzten thermodynamischen Systems eine schurkonvexe Funktion ist. Dabei bezeichnet pi die inverse Temperatur des i-ten Teilsystems. Falls die innere Energie proportional zu istwie etwa bei Spinsystemen inHochtemperatur-Naherungso folgt aus der Schurkonvexitat, daB beliebiger Temperaturausgleich zwischen den Teilsystemen stets zu einem Abfallen von Z(6) fuhrt.A b s t r a c t . We stress that the canonical pertition function Z(pl, , ! I2, ._., 8") = Z(8) of a tliermodynamical system consisting of n independent subsystems is a Schur-convex function. By pi the inverse temperature of the i-th subsystem is denoted. If the internal energy is proportional to pas e.g. for spin systems in the high temperature approximationthen from the Schur-convexity it follows that arbitrary temperature equalization between the subsystems can only diminish Z(p).

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On the Accessibility of States for Systems with Dissipative Dynamics

Zylka

1990

Annalen der Physik

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A b s t r a c t . We investigate certain dissipative dynamical systems from the aspect of the accessibility of states. Here the set of the n-dimensional probability vectors serves as state space, while i t is assumed that the dynamics can be modelled by generalized doubly stochastic matrices. We clarify what on these assumptions the set of states looks like starting from which a given state is accessible.

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Temperature Relaxation between Systems with Negative Kelvin Temperatures

Cited by 3 publications

References 5 publications

Relativistic Quantum Statistics in the Wigner Formalism and its Applications to the Toda Oscillator

Relativistic Quantum Statistics in the Wigner Formalism and its Applications to the Toda Oscillator

Über das monotone Verhalten gewisser Zustandssummen bei Temperaturausgleich

On the Accessibility of States for Systems with Dissipative Dynamics

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