cooking energy transitions. While the traditional energy ladder hypothesis suggests that households move from firewood to cleaner fuels as incomes rise, empirical evidence increasingly shows that this transition is neither smooth nor purely income-driven. Using NSSO consumption data and Census-based energy-use information for Bihar, this study shows that rural firewood consumption patterns exhibit significant nonlinear dependence, challenging the assumption of predictable and linear fuel transitions. Importantly, we clarify that statistical evidence is interpreted as nonlinear and complex dynamics, rather than deterministic chaos. We further estimate the Atkinson Energy Inequality Index across cooking fuels and find that inequality in access to modern cooking energy is substantial and varies by fuel type. Sensitivity analysis across inequality aversion parameters (ε = 0.3, 0.5, 0.9) confirms the robustness of these disparities. States with higher cooking-energy inequality tend to show slower improvements in clean fuel penetration and lower multidimensional development progress. Our findings suggest that rural energy transition is shaped not only by income but also by structural inequality and complex behavioral patterns. Policies focusing solely on subsidies or income growth are therefore insufficient. Instead, locally adaptive, inequality-sensitive, and behaviorally informed strategies are required to ensure equitable and sustainable clean cooking transitions.