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Passive states and KMS states for general quantum systems

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Abstract

We characterize equilibrium states of quantum systems by a condition of passivity suggested by the second principle of thermodynamics. Ground states and β-KMS states for all inverse temperatures β≧0 are completely passive. We prove that these states are the only completely passive ones. For the special case of states describing pure phases, assuming the passivity we reproduce the results of Haag et al.

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References

  1. Araki, H.: Lecture Notes at Varenna School, Summer 1973

  2. Araki, H.: On the equivalence of the KMS condition and the variational principle for quantum lattice systems. Commun. math. Phys.38, 1 (1974)

    Google Scholar 

  3. Araki, H.: Relative entropy of states of von Neumann algebra. Preprint RIMS 191 (1975)

  4. Araki, H., Sewell, G.L.: KMS condition and local thermodynamical stability of quantum lattice systems. Commun. math. Phys.52, 103 (1977)

    Google Scholar 

  5. Arveson, W.: On groups of automorphisms of operator algebras. J. Funct. Anal.15, 217 (1974)

    Google Scholar 

  6. Bratteli, O., Kastler, D.: Relaxing the clustering condition in the derivation of the KMS property. Commun. math. Phys.46, 37 (1976)

    Google Scholar 

  7. Connes, A.: Une classification des facteurs de type III. Ann. Sci. Ecole Norm. Sup.6, 133 (1973)

    Google Scholar 

  8. Haag, R., Kastler, D., Trych-Pohlmeyer, E. B.: Stability and equilibrium states. Commun. math. Phys.38, 173 (1974)

    Google Scholar 

  9. Kadison, R.V.: Some analytic methods in the theory of operator algebras. Lectures notes in mathematics, Vol. 140. Berlin-Heidelberg-New York: Springer 1970

    Google Scholar 

  10. Kastler, D.: Equilibrium states of matter and operator algebras. Proc. Roma Conf. onC*-algebras (1975)

  11. Uhlenbeck, G. E., Ford, G. W.: Lectures in statistical mechanics. Providence, Rhode Island: Am. Math. Soc. 1963

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Methods in Physics, University of Warsaw, PL-00-682, Warszawa, Poland

    W. Pusz & S. L. Woronowicz

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  1. W. Pusz
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  2. S. L. Woronowicz
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Communicated by H. Araki

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Pusz, W., Woronowicz, S.L. Passive states and KMS states for general quantum systems. Commun.Math. Phys. 58, 273–290 (1978). https://doi.org/10.1007/BF01614224

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