We propose a generalized free energy potential for active systems, including both stochastic master equations and deterministic nonlinear chemical reaction networks. Our generalized free energy is defined variationally as the "most irreversible" state observable. This variational principle is motivated from several perspectives, including large deviations theory, thermodynamic uncertainty relations, Onsager theory, and information-theoretic optimal transport. In passive systems, the most irreversible observable is the usual free energy potential and its irreversibility is the entropy production rate (EPR). In active systems, the most irreversible observable is the generalized free energy and its irreversibility gives the excess EPR, the nonstationary contribution to dissipation. The remaining "housekeeping" EPR is a genuine nonequilibrium contribution that quantifies the nonconservative nature of the forces. We derive far-from-equilibrium thermodynamic speed limits for excess EPR, applicable to both linear and nonlinear systems. Our approach overcomes several limitations of the steady-state potential and the Hatano-Sasa (adiabatic/nonadiabatic) decomposition, as we demonstrate in several examples.

翻译：我们提出了一种适用于活性系统的广义自由能势，涵盖随机主方程和确定性非线性化学反应网络。该广义自由能通过变分原理定义为“最不可逆”的状态可观测量。这一变分原理的动机源于多个理论视角，包括大偏差理论、热力学不确定性关系、Onsager理论以及信息论最优输运。在被动系统中，最不可逆可观测量即为通常的自由能势，其不可逆性表现为熵产生率（EPR）。在活性系统中，最不可逆可观测量是广义自由能，其不可逆性给出了超额EPR，即对耗散的非稳态贡献。剩余的“持家”EPR是真正的非平衡贡献，量化了力的非保守性质。我们推导了适用于线性和非线性系统的、远离平衡态的超额EPR热力学速度极限。我们的方法克服了稳态势和Hatano-Sasa（绝热/非绝热）分解的若干局限性，这将在多个示例中予以展示。