the same input does not always produce the same output. IN fact it's guaranteed not to for at least three reasons:

- repeatedly presenting the same input to a neuron has a response that depends on neurotransmitter reuptake rates. If the synapse isn't "recovered", you get a different spike rate out.

- neurons fire stochastically in the absence of stimulus. Responses to small stimuli are indistinguishable from noise.

- The above two phenomena propagate through connected series of neurons in a nonlinear way.

Right, but these properties don't make neurons acausal, it makes them stateful and sensitive to noise which is not explicitly modelled as an input in your view. You can model noise as a constant input variable though, which preserves causality, just not determinism.

see also, https://books.google.com/books?id=BUghCgAAQBAJ&pg=PA45&lpg=P...

They're a little neurotic.