References

1

 Daniel P. Aalberts and A. Nihat Berker. Spin-wave bound-state energies from an Ising model. Phys. Rev. B, 49(2):1073-1078, Jan 1994.

2

 Ryuzo Abe. Statistical Mechanics. University of Tokyo Press, Tokyo, 1975.

3

 Milton Abramowitz and Irene A. Stegun. Handbook of Mathematical Functions. Dover, New York, 1963.

4

 G. P. arin. On a statistical estimate for the entropy of a sequence of independent random variables. Theory Prob. Appl., 4(3):333-336, 1959.

5

 R. Balescu. Non-equilibrium statistical mechanics, chapter 5, pages 209-271. In Biel and Rae [9], 1972.

6

 R. J. Baxter. Exactly Solved Models in Statistical Mechanics. Academic Press, London, 1982.

7

 R. J. Baxter. Exactly Solved Models in Statistical Mechanics, chapter 1, page 1. Volume 1 of D'Ariano et al. [17], 5-64.

8

 Shahar Ben-Menahem. Spin-measurement retrodiction. Phys. Rev. A, 39(4):1621-1627, Feb 1989.

9

 J. Biel and J. Rae, editors. Irreversibility in the Many-Body Problem. Sitges International School of Physics, May, 1972. Plenum, New York, 1972.

10

 K. Binder and A. P. Young. Spin Glasses: Experimental facts, theoretical concepts, and open questions. Rev. Mod. Phys., 58(4):801-976, Oct 1986.

11

 J. De Boer and G. Uhlenbeck, editors. Studies in Statistical Mechanics, Vol. 1. Interscience Publishers, New York, 1961.

12

 N. Bogoliubov. Problems of Dynamical Theory in Statistical Physics, chapter 1, pages 5-118. In Boer and Uhlenbeck [11], 1961.

13

 R. Camassa, D. D. Holm, and J. M. Hyman. Adv. Appl. Mech., 31:1, 1994.

14

 H. S. Carslaw and J. C. Jaeger. Operational Methods in Applied Mathematics. Oxford University Press, London, England, 1953.

15

 Peter V. Coveney. The second law of thermodynamics: entropy, irreversibility, and dynamics. Nature, 333(2):409-415, Jun 1988.

16

 Thomas M. Cover and Joy A. Thomas. Elements of Information Theory. John Wiley and Sons, New York, 1991.

17

 G. M. D'Ariano, A. Montorosi, and M. G. Rasetti, editors. Integrable Systems in Statistical Mechanics, volume 1 of Series on Advances in Statistical Mechanics. Institute for Scientific Interchange, Torino, Italy, 1985.

18

 Morris H. DeGroot. Probability and Statistics. Addison Wesley, Reading, MA, 1984.

19

 Richard O. Duda. Pattern Classification and Scene Analysis. Wiley, New York, 1973.

20

 A. Elkouraychi, M. Saber, and J. W. Tucker. On the theory of the transverse Ising model with arbitrary spin. Physica A, 213:576-586, 1995.

21

 S. Eubank and D. Farmer. An Introduction to Chaos and Randomness. 1989.

22

 R. M. Fagen. Information measures: Statistical confidence limits and inference. J. Theor. Biol., 73:61-79, 1978.

23

 J. E. G. Farina. An elementary approach to quantum probability. American Journal of Physics, 61(5):466-468, May 1993.

24

 K. H. Fischer and J. A. Hertz. Spin Glasses. Cambridge University Press, Cambridge, UK, 1991.

25

 Daniel S. Fisher, Jeffrey M. Grinstein, and Anil Khurana. Theory of Random Magnets. Physics Today, pages 56-67, Dec 1988.

26

 I. Z. Fisher. Statistical Theory of Liquids. University of Chicago Press, Chicago, IL, 1964.

27

 C. W. Gardiner. Handbook of Stochastic Methods. Springer-Verlag, New York, 1990.

28

 Apostolos Gerasoulis. On the granularity and clustering of directed acyclic task graphs. IEEE Trans. Par. Dist. Sys., 4(6):686-702, Jun 1993.

29

 R. J. Glauber. J. Math. Phys., 4:294, 1963.

30

 Nigel Goldenfeld. Lectures on Phase Transitions and the Renormalization Group. Addison-Wesley, Reading, MA, 1992.

31

 P. Grassberger. Finite sample corrections to entropy and dimension estimates.Phys. Lett. A, 128:369-373, 1988.

32

 B. Harris. Colloq. Math. Societatis Janos Bolyai, 16:323-355, 1975.

33

 H. Herzel. Syst. Anal. Model. Simul., 5:435-444, 1988.

34

 H. Herzel, A. O. Schmitt, and W. Ebeling. Finite sample effects in sequence analysis. Tech. Report.

35

 Melvin J. Hinich. Higher Order Cumulants and Cumulant Spectra. Circ. Syst. Sig. Proc., 13(4):391-402, 1994.

36

 D. L. Holl, C. G. Maple, and B. Vinograde. Introduction to the Laplace Transform. Aplleton, New York, 1959.

37

 Henry B. Hollinger and Michael John Zenzen. The Nature of Irreversibility. D. Reidel Pub. Co., Dordrecht, 1985.

38

 Kerson Huang. Statistical Mechanics. John-Wiley and Sons, New York, 1987.

39

 Setsuo Ichimaru. Basic Principles of Plasma Physics. A Statistical Approach. Benjamin/Cummings, Reading, MA, 1973.

40

 John David Jackson. Classical Electrodynamics. Wiley, New York, 1975.

41

 E. Jen, editor. 1989 Lectures in Complex Systems, SFI Studies in the Sciences of Complexity, Lect. Vol. II, volume II of SFI Studies in the Sciences of Complexity. Addison-Wesley, 1990.

42

 Henrik Jeldtoft Jensen. 1/f Noise from diffusion in Lattice Gases. Mod. Phys. Lett. B, 5(9):625-634, 1991.

43

 Norman L. Johnson and Samuel Kotz. Discrete Distributions. John Wiley and Sons, New York, 1969.

44

 Shigetoshi Katsura. Statistical Mechanics of the Anisotropic Linear Heisenberg Model. Phys. Rev., 127(5):1508-1518, Dec 1962.

45

 Scott Kirkpatrick and David Sherrington. Infinite-ranged models of spin-glasses. Phys. Rev. B, 17(11):4384-4403, Jun 1978.

46

 Y. Kishimoto, T. Tajima, D. L. Fisher, and K. Mima. Cooling and Phase Control by Using laser-Undulator Beatwave. In Tajima [85], 1996.

47

 Charles Kittel. Introduction to Solid State Physics. John Wiley and Sons, New York, fifth edition, 1976.

48

 Charles Kittel. Quantum Theory of Solids. John Wiley and Sons, New York, 2nd edition, 1987.

49

 A.N. Kolmogorov and S.V. Fomin. Measure, Lebesgue Integrals, and Hilbert Space. Academic Press, New York, 1961.

50

 N. N. Lebedev. Special Functions and their Applications. Dover - Republication of the translation by Richard A. Silverman. Prentice, 1965, New York, 1972.

51

 T. Leonard and J. Hsu. Bayesian inference for a covariance matrix. Ann. Stat., 20:1669-1696, 1992.

52

 W. Li. Mutual information functions versus correlation functions. J. Stat. Phys., 60:823-837, 1990.

53

 Seth Lloyd. Use of mutual information to decrease entropy: Implications for the second law of thermodynamics. Phys. Rev. A, 39(10):5378-5386, 1989.

54

 Jon Mathews and R. L. Walker. Mathematical Methods of Physics. Benjamin/Cummings, Reading, MA, 1970.

55

 Richard D. Mattuck. A guide to Feynman diagrams in the many-body problem. McGraw-Hill, New York, 2nd edition, 1976.

56

 Barry M. McCoy, Jacques H. H. Perk, and Robert E. Schrock. Time-dependent correlation functions of the transverse Ising chain at the critical magnetic field. Nucl. Phys., B220([FS8]):35-47, 1983.

57

 Donald McQuarrie. Statistical Mechanics. Harper, 1973.

58

 Eugen Merzbacher. Quantum Mechanics. John Wiley and Sons, New York, 2nd edition, 1970.

59

 Albert Messiah. Quantum Mechanics, volume II. Wiley, New York, 1976.

60

 Marc Mezard, Giorgio Parisi, and Miguel Angel Virasoro. Spin Glass Theory and Beyond. World Scientific, New Jersey, 1987.

61

 G. A. Miller. Note on the Bias of Information Estimates, pages 95-100. 1955.

62

 Franz Mohling. Statistical Mechanics, Methods and Applications. John Wiley and Sons, New York, 1982.

63

 F. C. Moon. Chaotic Vibrations. Wiley, New York, 1987.

64

 Gerhard Muller and Robert E. Shrock. Dynamical correlation functions for one-dimensional quantum spin systems: New results based on a rigorous approach. J. Appl. Phys., 55(6):1874-1876, Mar 1984.

65

 Chrysostomos L. Nikias and Jerry M. Mendel. Signal processing with higher-order spectra. IEEE Signal Processing, pages 10-37, Jul 1993.

66

 Milan Palus. Identifying and quantifying chaos by using information theoretic functionals. In Time Series Prediction: Forecasting the Future and Understanding the Past, pages 387-414, 1992.

67

 V.S. Pugachev. Probability Theory and Mathematical Statistics for Engineers. Pergamon, New York, 1984.

68

 H. Quastler, editor. Information Theory in Psychology. Free Press, Glencoe, IL, 1955.

69

 L. E. Reichl. A Modern Course in Statistical Physics. University of Texas Press, Austin, Texas, 1980.

70

 H. Reiger and A. P. Young. Zero-Temperature Quantum Phase Transition of a Two-Dimensional Ising Spin Glass. Phys. Rev. Lett., 27(26):4141-4144, Jun 1994.

71

 Fazlollah M. Reza. An Introduction to Information Theory. Dover, New York, 1961.

72

 M. A. Ruderman and C. Kittel. Phys. Rev., 96:99, 1954.

73

 Walter Rudin. Priciples of Mathematical Analysis. McGraw-Hill, New York, 1976.

74

 Hidetsugu Sakaguchi. Renyi entropy and statistical mechanics. Prog. Theor. Phys., 81(4):732-737, Apr 1989.

75

 Hidetsugu Sakaguchi. Kolmogorov-Sinai Entropy of the Ising Model. Prog. Theor. Phys., 86(2):303-307, Aug 1991.

76

 J. J. Sakurai. Modern Quantum Mechanics. Benjamin/Cumings, Menlo Park, CA, 1985.

77

 A. O. Schmitt, H. Herzel, and W. Ebeling. A new method to calculate higher-order entropies from finite samples. Europhysics Letters, 23(5):303-309, 1993.

78

 Thomas D. Schneider. Theory of Molecular Machines. I. Channel Capacity of Molecular Machines. J. Theor. Biol., 148:83-123, 1991.

79

 Thomas D. Schneider. Theory of Molecular Machines. II. Energy Dissipation from Molecular Machines. J. Theor. Biol., 148:125-137, 1991.

80

 James B. Seaborn. Hypergeometric functions and their applications, volume 8 of Texts in applied mathematics. Springer-Verlag, New York, 1991.

81

 Claude E. Shannon and Warren Weaver. The Mathematical Theory of Communication. University of Illinois Press, Chicago, 1963.

82

 Barry Simon. Uniqueness of Phase Transition Temperature in Multidimensional Ising Models. Physics Today, pages s43-s44, Jan 86.

83

 H. Eugene Stanley. Introduction to Phase Transitions and Critical Phenomenoa. Oxford University Press, New York, 1971.

84

 T. Tajima. Computational Plasma Physics with Applications to Fusion and Astrophysics. Advanced Book Program. Addison-Wesley Pub. Co., Redwood City, CA, 1989.

85

 T. Tajima, editor. The Future of Accelerator Physics: The Tamura Symposium Proceedings. American Institute of Physics, New York, 1996.

86

 Minoru Takahashi. Analytical and Numerical Investigations of Spin Chains. Prog. Theor. Phys., 91(1):1-15, Jan 1994.

87

 Colin J. Thompson. Mathematical Statistical Mechanics. Princeton University Press, Princeton, NJ, 1972.

88

 Lev Vaidman, Yakir Aharonov, and David Z. Albert. How to ascertain the values of , , and  of a spin- particle. Phys. Rev. Lett., 58(14):1385-1387, Apr 1987.

89

 P. van Ede van der Pals and P. Gaspard. Two-dimensional quantum spin Hamiltonians: Spectral properties. Phys. Rev. E, 49(1):79-98, Jan 1994.

90

 J. H. van Lint and R. M. Wilson. A Course in Combinatorics. Cambridge University Press, New York, 1992.

91

 Richard F. Voss. Evolution of Long-Range Fractal Correlations and 1/f Noise in DNA Base Sequences. Phys. Rev. Lett., 68(25):3805-3808, Jun 1992.

92

 Gregory H. Wannier. Statistical Physics. Wiley, New York, 1966.

93

 Satoshi Watanabe. Pattern Recognition: Human and Mechanical. John Wiley and Sons, New York, 1985.

94

 Andreas S. Weigend and Neil A. Gershenfeld, editors. Time Series Prediction: Forecasting the Future and Understanding the Past. Proceedings of the NATO Advanced Research Workshop on Comparative Time Series Analysis held in Santa Fe, New Mexico, May 14-17, 1992, number XV in Santa Fe Institute Studies in the Sciences of Complexity. Addison-Wesley, 1994.

95

 D. R. Wolf and D. H. Wolpert. Estimating functions of probability distributions from finite samples, part 2: Mutual information, chi-squared. Los Alamos Unclassified Report, LA-UR-93-833(Send email to comp-gas@xyz.lanl.gov with subject ``get 9403002''), 1993.

96

 D. H. Wolpert and D. R. Wolf. Estimating functions of probability distributions from finite samples. Phys. Rev. E, 52(6):6841-6854, Dec 1995.

97

 Hubert P. Yockey. Information Theory and Molecular Biology. Cambridge University Press, Cambridge, UK, 1992.

98

 Yi-Cheng Zhang. Complexity and 1/f noise. A phase space approach. J. Phys. I France, 1:971-977, Jul 1991.

Tue Mar 25 08:11:49 CST 1997