用随机热力学重新解读生成模型，揭示其能量与熵的动态机制。
Stochastic Thermodynamics and SDE-based Generative Models
- 从随机热力学出发，定义路径级的功、热和熵产生。
- 推导出适用于时变温度与非保守力的广义Jarzynski关系式。
- 为扩散模型和Schrödinger桥提供非平衡统计力学视角，适合理论研究者。
基于随机微分方程（SDE）的生成模型，包括扩散模型和Schrödinger桥，在语音增强、图像修复和时间序列生成等信号处理任务中得到广泛应用。本文在随机热力学框架下构建了此类模型的建模体系。核心成果包括路径层面的功、热与熵产生的定义，以及广义的Jarzynski恒等式和类似热力学第二定律的不等式。该框架将原始的Jarzynski设定拓展至时变浴温与非保守驱动力的情形。这一热力学视角有望从非平衡统计力学角度深化对扩散模型和Schrödinger桥的理解。
原文摘要 · Abstract (English)
SDE-based generative models, including diffusion models and the Schrödinger bridge, have found broad applications in signal processing tasks such as speech enhancement, image restoration, and time-series generation. This note presents a modeling framework for such models within the context of stochastic thermodynamics. The main results of this note are trajectory-level definitions of work, heat, and entropy production, along with a generalized Jarzynski identity and a second-law-like inequality. The proposed framework extends the original Jarzynski setup to accommodate time-dependent bath temperature and nonconservative driving forces. This thermodynamic perspective may deepen our understanding of diffusion models and the Schrödinger bridge from a nonequilibrium statistical mechanics viewpoint.
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