A Fundamental Property of Quantum-Mechanical Entropy
There are some properties of entropy, such as concavity and subadditivity, that are known to hold (in classical and in quantum mechanics) irrespective of any assumptions on the detailed dynamics of a system. These properties are consequences of the definition of entropy as S(p) =—Trp lnp (quantum), (1a) S(p) =- f p lnp (classical continuous), (1b) S(p)= p i Inpi (classical discrete), (1c) where Tr means trace, p is a density matrix in (1a), and p is a distribution function (usually on R 6n) in (1b). In (1c) the p i are discrete energy level probabilities.
KeywordsDensity Matrix Pure State Generalize Entropy Physical Review Letter Arbitrary Region
Unable to display preview. Download preview PDF.
- 4.F. Bauman and R. Jost, in Problems of Theoretical Physics; Essays Dedicated to N. N. Bogoliubov (Nauka, Moscow, 1969), pp. 285–293.Google Scholar
- 7.R. Jost, in “Quanta”—Essays in Theoretical Physics Dedicated to Gregor Wentzel, edited by P. G. O. Freund, C. J. Goebel, and Y. Nambu (Univ. of Chicago Press, Chicago, 111., 1970), pp. 13–19.Google Scholar
- 8.E. H. Lieb, “Convex Trace Functions and Proof of the Wigner-Yanase-Dyson Conjecture” (to be published).Google Scholar
- 9.E. H. Lieb and M. B. Ruskai, “Proof of the Strong Subadditivity of Quantum Mechanical Entropy” (to be published).Google Scholar