Thermodynamics and signatures of criticality in a network of neurons

Gašper Tkačik, Thierry Mora, Olivier Marre, Dario Amodei, Stephanie E. Palmer, Michael J. Berry, William Bialek

Research output: Contribution to journalArticlepeer-review

144 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)11508-11513
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number37
StatePublished - Sep 15 2015

All Science Journal Classification (ASJC) codes

  • General


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