TY - JOUR

T1 - Shannon's information is not entropy

AU - Schiffer, Marcelo

N1 - Funding Information:
I am indebted to J.D. Bekenstein for calling my attention to this problem and for many enlightening conversations. I am also thankful to the Ben Gurion University for its hospitality and to CNPq for partial financial support. I wish to thank J. Daboul for showing me a flaw in a previous version of the manuscript.

PY - 1991/4/15

Y1 - 1991/4/15

N2 - Contrary to the widespread belief, Shannon's information and entropy are not in general equivalent. The purpose of this Letter is to discuss their conceptual difference and to pinpoint to mathematical reason for this. This fact is further illustrated through a toy model consisting of a harmonic oscillator in a coherent state, showing explicitly the dependence of Shannon's information on the class of quantum states the system is in. The interrelation between Shannon's information and entropy is reestablished after a theorem telling which class of states maximizes the (missing) information is proved. We shall conclude that entropy is the maximum amount of missing information.

AB - Contrary to the widespread belief, Shannon's information and entropy are not in general equivalent. The purpose of this Letter is to discuss their conceptual difference and to pinpoint to mathematical reason for this. This fact is further illustrated through a toy model consisting of a harmonic oscillator in a coherent state, showing explicitly the dependence of Shannon's information on the class of quantum states the system is in. The interrelation between Shannon's information and entropy is reestablished after a theorem telling which class of states maximizes the (missing) information is proved. We shall conclude that entropy is the maximum amount of missing information.

UR - http://www.scopus.com/inward/record.url?scp=44949279211&partnerID=8YFLogxK

U2 - 10.1016/0375-9601(91)90033-5

DO - 10.1016/0375-9601(91)90033-5

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AN - SCOPUS:44949279211

SN - 0375-9601

VL - 154

SP - 361

EP - 365

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 7-8

ER -