<![CDATA[The emergence of variational quantum machines (VQMs) has introduced new paradigms for quantum learning by combining quantum computational advantages with classical optimization strategies. However, the physical resources required during the learning process remain insufficiently understood, particularly from the perspective of thermodynamic efficiency. This study develops an information-theoretic framework to analyze the thermodynamic cost of learning in variational quantum systems by establishing relationships between information acquisition, parameter optimization, entropy variation, and energy dissipation. The proposed framework integrates principles from quantum information theory and nonequilibrium thermodynamics to quantify the minimum energetic requirements associated with updating quantum models during training. The analysis demonstrates that learning efficiency in VQMs is fundamentally constrained by information processing limits, where reductions in uncertainty and improvements in model performance correspond to measurable thermodynamic expenditures. The framework provides a theoretical foundation for evaluating the sustainability and scalability of future quantum learning architectures. This research contributes a new perspective by linking quantum machine learning performance with physical resource consumption, offering insights for designing energy-efficient quantum artificial intelligence systems.]]>
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