  Neural dynamics of energy-based models are governed by energy minimization
and the patterns stored in the network are retrieved when the system reaches
equilibrium. However, when the system is driven by time-varying external input,
the nonequilibrium process of such physical system has not been well
characterized. Here, we study attractor neural networks, specifically the
Hopfield network, driven by time-varying external input and measure
thermodynamic quantities along trajectories between two collective states. The
overlap between distribution of the forward and reversal work along the
nonequilibrium trajectories agrees with the equilibrium free energy difference
between two states, following the prediction of Crooks fluctuation theorem. We
study conditions with different stimulation protocol and neural network
constraints. We further discuss how biologically plausible synaptic connections
and information processing may play a role in this nonequilibrium framework.
These results demonstrate how nonequilibrium thermodynamics can be relevant for
neural computation and connect to recent systems neuroscience studies with
closed-loop dynamic perturbations.

Neurons and Cognition;Biological Physics