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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Physik & Astronomie Theoretische Physik A Statistical Mechanical Interpretation of Algorithmic Information Theory
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A Statistical Mechanical Interpretation of Algorithmic Information Theory
Kohtaro Tadaki (Broschiert, Englisch)
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Beschreibung
This book is the first one that provides a solid bridge between algorithmic information theory and statistical mechanics. Algorithmic information theory (AIT) is a theory of program size and recently is also known as algorithmic randomness. AIT provides a framework for characterizing the notion of randomness for an individual object and for studying it closely and comprehensively. In this book, a… statistical mechanical interpretation of AIT is introduced while explaining the basic notions and results of AIT to the reader who has an acquaintance with an elementary theory of computation. A simplification of the setting of AIT is the noiseless source coding in information theory. First, in the book, a statistical mechanical interpretation of the noiseless source coding scheme is introduced. It can be seen that the notions in statistical mechanics such as entropy, temperature, and thermal equilibrium are translated into the context of noiseless source coding in a natural manner. Then, the framework of AIT is introduced. On this basis, the introduction of a statistical mechanical interpretation of AIT is begun. Namely, the notion of thermodynamic quantities, such as free energy, energy, and entropy, is introduced into AIT. In the interpretation, the temperature is shown to be equal to the partial randomness of the values of all these thermodynamic quantities, where the notion of partial randomness is a stronger representation of the compression rate measured by means of program-size complexity. Additionally, it is demonstrated that this situation holds for the temperature itself as a thermodynamic quantity. That is, for each of all the thermodynamic quantities above, the computability of its value at temperature T gives a sufficient condition for T to be a fixed point on partial randomness. In this groundbreaking book, the current status of the interpretation from both mathematicaland physical points of view is reported. For example, a total statistical mechanical interpretation of AIT that actualizes a perfect correspondence to normal statistical mechanics can be developed by identifying a microcanonical ensemble in the framework of AIT. As a result, the statistical mechanical meaning of the thermodynamic quantities of AIT is clarified. In the book, the close relationship of the interpretation to Landauer's principle is pointed out. 69,54 €
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Technische Daten
Erscheinungsdatum
21.11.2019
Sprache
Englisch
EAN
9789811507380
Herausgeber
Springer Singapore
Serien- oder Bandtitel
SpringerBriefs in Mathematical Physics
Sonderedition
Nein
Autor
Kohtaro Tadaki
Seitenanzahl
136
Einbandart
Broschiert
Schlagwörter
Algorithmic information theory, Statistical mechanics, Temperature, Compression rate, Thermodynamic quantities
Thema-Inhalt
PHU - Mathematische Physik
UMB - Algorithmen und Datenstrukturen
GPF - Informationstheorie
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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