Uncovering the underlying biophysical principles of emergent collective computational abilities, such as working memory, in neural circuits is one of the most essential concerns in modern neuroscience. Working memory system is often desired to be robust against noises. Such systems can be highly flexible for adapting environmental demands. How neural circuits reconfigure themselves according to the cognitive task requirement remains unclear. Previous studies explored the robustness and the

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... bility in working memory by tracing individual dynamical trajectories in a limited time scale, where the accuracy of the results depends on the volume of the collected statistical data. Inspired by thermodynamics and statistical mechanics in physical systems, we developed a non-equilibrium landscape and flux framework for studying the neural network dynamics. Applying this approach to a biophysically based working memory model, we investigated how changes in the recurrent excitation mediated by slow NMDA receptors within a selective population and mutual inhibition mediated by GABAergic interneurons between populations affect the robustness against noises. This is realized through quantifying the underlying non-equilibrium potential landscape topography and the kinetics of state switching. We found that an optimal compromise for a working memory circuit between the robustness and the flexibility can be achieved through the emergence of an intermediate state between the working memory states. An optimal combination of both increased self-excitation and inhibition can enhance the flexibility to external signals without significantly reducing the robustness to the random fluctuations. Furthermore, we found that the enhanced performance in working memory is supported by larger energy consumption. Our approach can facilitate the design of new network structure for cognitive functions with the optimal balance between performance and cost. Our work also provides a new paradigm for exploring the underlying mechanisms of many cognitive functions based on non-equilibrium physics.