The architectural features of efficient navigation in Energy Landscapes

Energy landscapes provide a powerful framework for studying stability in systems from biomolecular folding to fitness landscapes and machine learning optimization. In these systems, search efficiency can be quantified by the mean first passage time (MFPT) to the global minimum, averaged over all initial states. Though often rugged, with numerous minima and barriers hindering access to the ground state, many physical systems achieve low search times, suggesting optimized landscape architectures. To uncover this efficiency, we model energy landscapes as networks, with nodes as energy minima and edges as transition pathways with temperature-dependent Arrhenius rates. Contrary to intuition that highly connected landscapes avoid trap states and improve global minimum accessibility, we find that creating pathways by reducing infinite barriers isolating states can paradoxically increase ground-state search time. Notably, we establish a lower bound for MFPT, showing search efficiency depends primarily on the ground state's energy and connectivity.