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We propose a systematic method based on reinforcement learning (RL)techniques to find the optimal path that can minimize the total entropyproduction between two equilibrium states of open systems at the sametemperature in a given fixed time period. Benefited from the generalization ofthe deep RL techniques, our method can provide a powerful tool to address thisproblem in quantum systems even with two-dimensional continuous controllableparameters. We successfully apply our method on the classical and quantumtwo-level systems.

Reinforcement Learning Approach to Shortcuts between Thermodynamic States with Extra Constraints