Typical support and Sanov large deviations of correlated states

被引：17

作者：

Bjelakovic, Igor ^{[1
,3
]}

Deuschel, Jean-Dominique ^{[1
]}

Krueger, Tyll ^{[1
,2
,4
]}

Seiler, Ruedi ^{[1
]}

Siegmund-Schultze, Rainer ^{[1
,2
]}

Szkola, Arleta ^{[1
,2
]}

机构：

[1] Tech Univ Berlin, Fak Math & Naturwissensch 2, Inst Math, D-10623 Berlin, Germany

[2] Max Planck Inst Math Sci, D-04103 Leipzig, Germany

[3] Tech Univ Berlin, Heinrich Hertz Chair Mobile Commun, Werner Von Siemens Bau HFT 6, D-10587 Berlin, Germany

[4] Univ Bielefeld, Fak Phys, D-33619 Bielefeld, Germany

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2008年 / 279卷 / 02期

关键词：

D O I：

10.1007/s00220-008-0440-6

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Discrete stationary classical processes as well as quantum lattice states are asymptotically confined to their respective typical support, the exponential growth rate of which is given by the (maximal ergodic) entropy. In the iid case the distinguishability of typical supports can be asymptotically specified by means of the relative entropy, according to Sanov's theorem. We give an extension to the correlated case, referring to the newly introduced class of HP-states.

引用

页码：559 / 584

页数：26

共 26 条

[1]

[Anonymous], 1969, STAT MECH

[2] A quantum version of Sanov's theorem [J].

Bjelakovic, I ;

Deuschel, JD ;

Krüger, T ;

Seiler, R ;

Siegmund-Schultze, R ;

Szkola, A .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2005, 260 (03) :659-671

[3] An ergodic theorem for the quantum relative entropy [J].

Bjelakovic, I ;

Siegmund-Schultze, R .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2004, 247 (03) :697-712

[4] The Shannon-McMillan theorem for ergodic quantum lattice systems [J].

Bjelakovic, I ;

Krüger, T ;

Siegmund-Schultze, R ;

Szkola, A .

INVENTIONES MATHEMATICAE, 2004, 155 (01) :203-222

[5]

Blum J.R., 1963, Z WAHRSCHEINLICHKEIT, V2, P1

[6] Basic Properties of Strong Mixing Conditions. A Survey and Some Open Questions [J].

Bradley, Richard C. .

PROBABILITY SURVEYS, 2005, 2 :107-144

[7]

Bratteli O., 1979, Operator Algebras and Quantum Statistical Mechanics, V1

[8]

Cover TM, 2006, Elements of Information Theory

[9] Quantum macrostates, equivalence of ensembles, and an H-theorem [J].

De Roeck, Wojciech ;

Maes, Christian ;

Netocny, Karel .

JOURNAL OF MATHEMATICAL PHYSICS, 2006, 47 (07)

[10]

DEUSCHEL J. D., 2001, LARGE DEVIATIONS

← 1 2 3 →