左）二維 AOUP 旋轉子示意圖。主動雜訊可視為熱浴的一部分。（右）四維白雜訊旋轉子示意圖。主動雜訊可視為一個粒子，浸沒於兩個彼此獨立、作用於膠體微粒的白雜訊熱浴之中。
符合熱力學第二定律之主動熱浴熱機描述
Phys. Rev. Research 8, 023136
Yi-Hung Liao, Jerard Vincent Ang, Pik-Yin Lai, and Yonggun Jun
Second law-abiding-account of heat engines in active bath
熱力學第二定律對能量轉換設下基本限制，例如卡諾效率上限。主動熱浴中若出現看似違反該限制的現象，通常與對熱庫能量學的考量不夠完整有關。若在布朗旋轉子模型中，將主動雜訊明確納入為獨立自由度，則可證明系統的熵產生仍維持非負，且卡諾極限依然成立。本研究顯示，只要將主動漲落正確納入熱力學描述，即可維持基本熱力學原理的適用性。
The second law of thermodynamics imposes limits on energy conversion, such as the Carnot bound. Apparent violations in active baths often arise from incomplete accounting of the reservoir's energetics. By treating active noise as an explicit degree of freedom in a Brownian gyrator model, we show that entropy production remains non-negative and the Carnot limit is preserved. This study demonstrates that properly accounting for active fluctuations as distinct thermodynamic components upholds fundamental principles.