It might be related to spatiotemporal scale, since nonequilibrium systems exhibit local thermodynamic equilibrium (sec 3.2 of this https://courses.physics.ucsd.edu/2020/Fall/physics210b/Non-Eqbrm%20Thermo_Demirel%20and%20Gerbaud.pdf says it's common in simpler nonequilibrium systems, though it is also found in more complicated active matter systems such as bird flocks https://doi.org/10.1038/nphys3846 ). Even though the whole nervous system must be a dissipative nonequilibrium system, at the microscopic scales of smaller networks this might be okay to ignore without too much consequence, but idk if that's a good idea if the aim is biological realism.
This paper shows that some biological dynamics only appear in ANNs if they are in nonequilibrium states due to asymmetric connections, which are common in bioNNs. https://www.pnas.org/doi/10.1073/pnas.1310692110 These dynamics include oscillations (traveling waves?) and free energy minimization, which aren't present in the symmetric Hopfield networks they tested