Kolmogorov's development of an information measure for problems of symbol-sequence
type was followed by numerous mathematically-oriented applications in computer
science and to models of randomness, many of these by Chaitin (Ref.118).
During the past decade, however, various models of physical systems have
been analyzed with these tools, and are noted below. Efforts to relate
such `microscopic' entropies to Shannon's measure and thermodynamic entropy
have been made, and remain an area of current research. These approaches
to the many-body problem are close in philosophy to that of Boltzmann's
H-function and H-theorem. It is not yet clear whether such
microscopic functions will suffer the same fate as H -- namely,
that they become unrelated to thermodynamic entropy in any system with
substantial potential energy (Ref.117).
112.``Three Approaches to the Quantitative Definition of Information,"
A.N. Kolmogorov, Probl. Inf. Trans. 1, 3-11 (1965). (A)
113.``Logical Basis for Information Theory and Probability Theory,"
A.N. Kolmogorov, IEEE Trans. IT-14, 662-664 (1968). (I)
114.``A Formal Theory of Inductive Inference. I, II.,"R.J.
Solmonoff, Inform. and Control 7, 1-22, 224-254 (1964). (A)
115.``On the length of programs for computing binary sequences,"G.J.
Chaitin, J. Assoc. Comput. Mach. 13, 547-569 (1966). (A)
116.``Microscopic and macroscopic entropy,"K. Lindgren,
Phys. Rev. A 38, 4794-4798 (1988). (A)
117.``Violation of Boltzmann's H-theorem in real gases,"
E.T. Jaynes, Phys. Rev. A4, 747-750 (1971). (I)
118.Algorithmic Information Theory, G.J. Chaitin (Cambridge
University Press, Cambridge, 1987. (A)
119.``Thermodynamic cost of computation, algorithmic complexity
and the information metric," W.H. Zurek, Nature 341, 119-124
(1989). (A)
120.``Algorithmic treatment of the spin-echo effect," S.
Lloyd and W.H. Zurek, J. Stat. Phys. 62, 819-839 (1991). (A)
121.``Complexity in quantum systems," A. Crisanti, M. Falcioni,
and A. Vulpiani, Phys. Rev. E 50, 138-144 (1994). An application
of information complexity to a spin-
particle in a magnetic field, where the Shannon entropy vanishes. (A)
122.``Information entropy, chaos and complexity of the shell-model
eigenvectors," V. Zelevinsky, M. Horoi, and B.A. Brown, Phys. Letters
B 350, 141-146 (1995). (A)
123.``Algorithmic Complexity of a Schwarzschild Black Hole,"
V.D. Dzhunnshaliev, Russian Physics Journal 38, 317-319 (1995).
(A)
124.``Algorithmic complexity of a protein," D.T. Gregory,
Phys. Rev. E 54, R39-R41 (1996). (A)
particle in a magnetic field, where the Shannon entropy vanishes. (A)