Complexity Measures and Physical Principles

  • Karoline Wiesner
Part of the Emergence, Complexity and Computation book series (ECC, volume 14)


I summarise some recent results on physics of information and discuss their impact on our understanding of complexity. A surprisingly coherent picture of measures of complexity, information theoretic functions, and thermodynamical quantities arises.


Mutual Information Relative Entropy Complexity Measure Physical Review Letter Predictive Information 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Benenson, Y., Adar, R., Paz-Elizur, T., Livneh, Z., Shapiro, E.: DNA molecule provides a computing machine with both data and fuel. Proceedings of the National Academy of Sciences 100(5), 2191–2196 (2003)CrossRefGoogle Scholar
  2. 2.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory. WileyBlackwell (2006)Google Scholar
  3. 3.
    Crooks, G.E.: Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. Physical Review E 60(3), 2721–2726 (1999)CrossRefGoogle Scholar
  4. 4.
    Crutchfield, J.P., Feldman, D.P.: Regularities unseen, randomness observed: Levels of entropy convergence. Chaos 13(1), 25–54 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Crutchfield, J.P., Young, K.: Inferring statistical complexity. Physical Revue Letters 63(2), 105 (1989)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Crutchfield, J.P., Ellison, C.J., Mahoney, J.R.: Time’s barbed arrow: Irreversibility, crypticity, and stored information. Physical Review Letters 103(9), 94101–94104 (2009)CrossRefGoogle Scholar
  7. 7.
    Friston, K., Kilner, J., Harrison, L.: A free energy principle for the brain. Journal of Physiology-Paris 100(1-3), 70–87 (2006)CrossRefGoogle Scholar
  8. 8.
    Grassberger, P.: Toward a quantitative theory of self-generated complexity. International Journal of Theoretical Physics 25(9), 907–938 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Gu, M., Wiesner, K., Rieper, E., Vedral, V.: Quantum mechanics can reduce the complexity of classical models. Nature Communications 3, 762 (2012)CrossRefGoogle Scholar
  10. 10.
    Jarzynski, C.: Nonequilibrium equality for free energy differences. Physical Review Letters 78(14), 2690–2693 (1997)CrossRefGoogle Scholar
  11. 11.
    Ladyman, J., Lambert, J., Wiesner, K.: What is a complex system? European Journal for Philosophy of Science 3(1), 33–67 (2013)CrossRefzbMATHGoogle Scholar
  12. 12.
    Monras, A., Beige, A., Wiesner, K.: Hidden quantum markov models and non-adaptive read-out of many-body states. Applied Mathematical and Computational Sciences 3, 93 (2011)zbMATHMathSciNetGoogle Scholar
  13. 13.
    Shalizi, C.R., Crutchfield, J.P.: Computational mechanics: Pattern and prediction, structure and simplicity. Journal of Statistical Physics 104(3), 817–879 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Still, S.: Information bottleneck approach to predictive inference. Entropy 16(2), 968–989 (2014)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Still, S., Crutchfield, J.P.: Structure or noise? arXiv/0708.0654 (2007)Google Scholar
  16. 16.
    Still, S., Crutchfield, J.P., Ellison, C.J.: Optimal causal inference: Estimating stored information and approximating causal architecture. arXiv/0708.1580 (2007)Google Scholar
  17. 17.
    Still, S., Sivak, D.A., Bell, A.J., Crooks, G.E.: Thermodynamics of prediction. Physical Review Letters 109(12), 120604 (2012)CrossRefGoogle Scholar
  18. 18.
    Tishby, N., Pereira, F.C., Bialek, W.: The information bottleneck method. arXiv/physics/0004057 (2000)Google Scholar
  19. 19.
    Wiesner, K., Gu, M., Rieper, E., Vedral, V.: Information-theoretic lower bound on energy cost of stochastic computation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 468(2148), 4058–4066 (2012)CrossRefMathSciNetGoogle Scholar
  20. 20.
    Zurek, W.H. (ed.): Information, physics, quantum: The search for links. Santa Fe Institute Studies in the Sciences of Complex Systems, vol. 8. Advanced Book Programme (1990)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Karoline Wiesner
    • 1
  1. 1.School of MathematicsUniversity of BristolBristolU.K.

Personalised recommendations