The essential nonlinearity ofN-level quantum thermodynamics

This paper explores the possibility that linear dynamical maps might be used to describe the energy-conserving, entropy-increasing motions which occur in closed thermodynamic systems as they approach canonical thermal equilibrium. ForN-level quantum systems withN>2, we prove that no such maps exist which are independent of the initial state.

[1]  Elias P. Gyftopoulos,et al.  A unified quantum theory of mechanics and thermodynamics. Part IIa. Available energy , 1976 .

[2]  Elias P. Gyftopoulos,et al.  A unified quantum theory of mechanics and thermodynamics. Part I. Postulates , 1976 .

[3]  William Band,et al.  Generalized two-level quantum dynamics. III. Irreversible conservative motion , 1978 .

[4]  W. Band,et al.  Generalized two-level quantum dynamics. I. Representations of the Kossakowski conditions , 1977 .

[5]  James L. Park,et al.  The physics and the semantics of quantum measurement , 1973 .

[6]  R. Ingarden,et al.  On the connection of nonequilibrium information thermodynamics with non-hamiltonian quantum mechanics of open systems , 1975 .

[7]  D. Frankl.  Foundations of classical and quantum statistical mechanics , 1967 .

[8]  James L. Park,et al.  On completely positive maps in generalized quantum dynamics , 1981 .

[9]  G. Lindblad.  On the generators of quantum dynamical semigroups , 1976 .

[10]  Elias P. Gyftopoulos,et al.  A unified quantum theory of mechanics and thermodynamics. Part III. Irreducible quantal dispersions , 1976 .

[11]  G. Hatsopoulos,et al.  A unified quantum theory of mechanics and thermodynamics. Part IIb. Stable equilibrium states , 1976 .

[12]  E. Sudarshan,et al.  Completely Positive Dynamical Semigroups of N Level Systems , 1976 .

[13]  Alfred Landé,et al.  New Foundations of Quantum Mechanics , 1966 .

[14]  J. Blatt.  An Alternative Approach to the Ergodic Problem , 1959 .

[15]  A. Kossakowski,et al.  On quantum statistical mechanics of non-Hamiltonian systems , 1972 .

[16]  R. Morrow,et al.  Foundations of Quantum Mechanics , 1968 .