In genuine nonequilibrium systems that undergo continuous driving, the thermodynamic forces are nonconservative, meaning they cannot be described by any free energy potential. Nonetheless, we show that the dynamics of such systems are governed by a "generalized free energy" that is derived from a large-deviations variational principle. This variational principle also yields a decomposition of fluxes, forces, and dissipation (entropy production) into a conservative "excess" part and a nonconservative "housekeeping" part. Our decomposition is universally applicable to stochastic master equations, deterministic chemical reaction networks, and open systems. We also show that the excess entropy production obeys a thermodynamic speed limit (TSL), a fundamental thermodynamic constraint on the rate of state evolution and/or external fluxes. We demonstrate our approach on several examples, including real-world metabolic networks, where we derive fundamental dissipation bounds and uncover "futile" metabolic cycles. Our generalized free energy and decomposition are empirically accessible to thermodynamic inference in both stochastic and deterministic systems. We discuss important connections to several theoretical frameworks, including information geometry and Onsager theory, as well as previous excess/housekeeping decompositions.

翻译：在经历连续驱动的真实非平衡系统中，热力学力是非保守的，这意味着它们无法用任何自由能势描述。尽管如此，我们证明了此类系统的动力学受一个从大偏差变分原理导出的"广义自由能"所支配。该变分原理还进一步将通量、力与耗散（熵产生）分解为保守的"超额"部分与非保守的"持家"部分。我们的分解普遍适用于随机主方程、确定性化学反应网络以及开放系统。我们还证明了超额熵产生遵循热力学速度极限（TSL），这是对状态演化和/或外部通量速率的基本热力学约束。我们在多个实例中展示了该方法，包括真实世界的代谢网络，并由此推导出基本的耗散界限并揭示了"无效"代谢循环。我们的广义自由能与分解在随机和确定性系统中均可通过热力学推断进行经验性获取。我们讨论了与多个理论框架的重要联系，包括信息几何与昂萨格理论，以及先前的超额/持家分解。