Nonequilibrium Green's functions for functional connectivity in the brain*

A theoretical framework describing the set of interactions between neurons in the brain, or functional connectivity, should include dynamical functions representing the propagation of signal from one neuron to another. Green's functions and response functions are natural candidates for this but, while they are conceptually very useful, they are usually defined only for linear time-translationally invariant systems. The brain, instead, behaves nonlinearly and in a time-dependent way. In this talk, I will show how nonequilibrium Green's functions can be used to describe the time-dependent functional connectivity of a continuous-variable network of neurons. I will show how the connectivity is related to the measurable response functions, and present illustrative numerical calculations inspired from C. elegans.