A statistical mechanical interpretation of algorithmic information theory. (2019)
- Record Type:
- Book
- Title:
- A statistical mechanical interpretation of algorithmic information theory. (2019)
- Main Title:
- A statistical mechanical interpretation of algorithmic information theory
- Further Information:
- Note: Kohtaro Tadaki.
- Authors:
- Tadaki, Kohtaro
- Contents:
- Intro; Preface; Contents; 1 Statistical Mechanical Interpretation of Noiseless Source Coding; 1.1 Introduction; 1.2 Instantaneous Codes; 1.3 Equilibrium Statistical Mechanics; 1.4 Statistical Mechanical Interpretation; 1.5 Properties of Statistical Mechanical Entropy; 1.6 Thermal Equilibrium Between Two Instantaneous Codes; 1.7 Dimension of Coded Messages; 1.8 Toward a Statistical Mechanical Interpretation of AIT; 2 Algorithmic Information Theory; 2.1 Basic Notation and Definitions; 2.2 Computability; 2.3 Prefix-Free Machines and Program-Size Complexity 5.1 Self-Referential Nature of Temperature5.2 Fixed Point Theorems by Thermodynamic Quantities of AIT; 5.3 The Proofs of the Fixed Point Theorems; 5.3.1 The Proof of Theorem 5.7; 5.3.2 The Proof of Theorem 5.8; 5.3.3 The Proof of Theorem 5.9; 5.3.4 Another Proof of Theorem 5.1 Based on the General Scheme; 5.4 Some Properties of the Sufficient Conditions; 5.5 Thermodynamic Quantities Based on an Arbitrary Optimal Prefix-Free Machine; 6 Statistical Mechanical Meaning of the Thermodynamic Quantities of AIT; 6.1 Perfect Correspondence to Normal Statistical Mechanics 6.2 Total Statistical Mechanical Interpretation of AIT6.3 Future Direction; 7 The Partial Randomness of Recursively Enumerable Reals; 7.1 R.E. Reals and Thermodynamic Quantities of AIT; 7.2 Previous Results on the Randomness of an R.E. Real; 7.3 Extension over the Notion of Partial Randomness; 7.4 The Completion of the Proof of Theorem 7.5; 7.5 Characterizations ofIntro; Preface; Contents; 1 Statistical Mechanical Interpretation of Noiseless Source Coding; 1.1 Introduction; 1.2 Instantaneous Codes; 1.3 Equilibrium Statistical Mechanics; 1.4 Statistical Mechanical Interpretation; 1.5 Properties of Statistical Mechanical Entropy; 1.6 Thermal Equilibrium Between Two Instantaneous Codes; 1.7 Dimension of Coded Messages; 1.8 Toward a Statistical Mechanical Interpretation of AIT; 2 Algorithmic Information Theory; 2.1 Basic Notation and Definitions; 2.2 Computability; 2.3 Prefix-Free Machines and Program-Size Complexity 5.1 Self-Referential Nature of Temperature5.2 Fixed Point Theorems by Thermodynamic Quantities of AIT; 5.3 The Proofs of the Fixed Point Theorems; 5.3.1 The Proof of Theorem 5.7; 5.3.2 The Proof of Theorem 5.8; 5.3.3 The Proof of Theorem 5.9; 5.3.4 Another Proof of Theorem 5.1 Based on the General Scheme; 5.4 Some Properties of the Sufficient Conditions; 5.5 Thermodynamic Quantities Based on an Arbitrary Optimal Prefix-Free Machine; 6 Statistical Mechanical Meaning of the Thermodynamic Quantities of AIT; 6.1 Perfect Correspondence to Normal Statistical Mechanics 6.2 Total Statistical Mechanical Interpretation of AIT6.3 Future Direction; 7 The Partial Randomness of Recursively Enumerable Reals; 7.1 R.E. Reals and Thermodynamic Quantities of AIT; 7.2 Previous Results on the Randomness of an R.E. Real; 7.3 Extension over the Notion of Partial Randomness; 7.4 The Completion of the Proof of Theorem 7.5; 7.5 Characterizations of the Dimension of an R.E. Real; 7.6 Further Properties of T-Convergence; 7.7 Future Direction; 8 Computation-Theoretic Clarification of the Phase Transition at Temperature T=1 8.1 Computational Complexity-Theoretic Treatment in Computability Theory8.2 Turing Machine Computing a Prefix-Free Machine; 8.3 Reducibility in Query Size f; 8.4 Unidirectionality; 8.4.1 The Proof of Theorem 8.4; 8.4.2 The Proof of Theorem 8.5; 8.5 T-Convergent R.E. Reals and Strict T-Compressibility; 8.6 Bidirectionality; 8.6.1 The Proof of Theorem 8.19; 8.6.2 The Proof of Theorem 8.20; 8.7 Concluding Remarks; 9 Other Related Results and Future Development; 9.1 Current Status of the Research; 9.1.1 Clarification of the Property of Fixed Points by Statistical Mechanical Technique … (more)
- Publisher Details:
- Singapore : Springer
- Publication Date:
- 2019
- Extent:
- 1 online resource (xi, 136 pages), illustrations
- Subjects:
- 531.01/5195
Statistical mechanics
Electronic books
Electronic books - Languages:
- English
- ISBNs:
- 9789811507397
9811507392 - Related ISBNs:
- 9789811507380
- Notes:
- Note: Includes bibliographical references and index.
Note: Online resource; title from PDF title page (SpringerLink, viewed November 18, 2019). - Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
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- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.471674
- Ingest File:
- 02_620.xml