Thermodynamics and signatures of criticality in a network of neurons

Proc Natl Acad Sci U S A. 2015 Sep 15;112(37):11508-13. doi: 10.1073/pnas.1514188112. Epub 2015 Sep 1.


The activity of a neural network is defined by patterns of spiking and silence from the individual neurons. Because spikes are (relatively) sparse, patterns of activity with increasing numbers of spikes are less probable, but, with more spikes, the number of possible patterns increases. This tradeoff between probability and numerosity is mathematically equivalent to the relationship between entropy and energy in statistical physics. We construct this relationship for populations of up to N = 160 neurons in a small patch of the vertebrate retina, using a combination of direct and model-based analyses of experiments on the response of this network to naturalistic movies. We see signs of a thermodynamic limit, where the entropy per neuron approaches a smooth function of the energy per neuron as N increases. The form of this function corresponds to the distribution of activity being poised near an unusual kind of critical point. We suggest further tests of criticality, and give a brief discussion of its functional significance.

Keywords: Monte Carlo; correlation; entropy; information; neural networks.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Algorithms
  • Animals
  • Brain / physiology*
  • Entropy
  • Hot Temperature
  • Models, Neurological
  • Models, Statistical
  • Monte Carlo Method
  • Nerve Net
  • Neurons / physiology*
  • Probability
  • Reproducibility of Results
  • Retina / physiology
  • Thermodynamics
  • Urodela