近日，英国剑桥大学Sarah A. M. Loos团队研究了非平衡稳态之间的最优过渡。该项研究成果发表在2025年9月15日出版的《美国科学院院刊》杂志上。

微观尺度上有限时间过程的最优控制具有重要的理论和实践意义，特别是对于纳米机器的节能运行。虽然以前的研究主要集中在平衡状态之间的过渡，但许多生物和技术相关的过程发生在远离平衡的地方。在这种非平衡状态下，记忆——现实系统中无处不在的特征——扮演着复杂的角色，因为任何驱动都必然会激发内部记忆模式。这激发了对非平衡状态下最优控制策略的深入探索。

研究组结合实验、理论和计算方法来研究一个胶态粒子在两个非平衡稳态（NESS）之间的跃迁。他们确定了在两个NESS之间的有限时间过渡期间最小化热力学功的最优控制协议。研究组比较了粘质和粘弹性流体环境中的最佳方案，这在现实的技术和生物过程中很常见，并且由于延迟响应而引入记忆。不考虑记忆效应的存在，最佳方案始终平衡能量提取与耗散最小化。在有内存的情况下，如果协议与环境的时间响应相匹配，则实现最优控制。这些发现为设计复杂环境中有限时间非平衡过程的最优控制策略提供了关键见解。

附：英文原文

Title: Optimal transitions between nonequilibrium steady states

Author: Monter, Samuel, Loos, Sarah A. M., Bechinger, Clemens

Issue&Volume: 2025-9-15

Abstract: The optimal control of finite-time processes on the microscale is of significant theoretical and practical interest, particularly for the energy-efficient operation of nanomachines. While previous studies have primarily focused on transitions between equilibrium states, many biologically and technologically relevant processes occur far from equilibrium. In such nonequilibrium settings, memory, a ubiquitous feature in realistic systems, plays an intricate role, as any driving necessarily excites internal memory modes. This motivates a deeper exploration of optimal control strategies in nonequilibrium regimes. Here, we combine experiments, theory, and computational methods to investigate the transition of a colloidal particle confined in an optical trap between two nonequilibrium steady states (NESS). We identify optimal control protocols that minimize the thermodynamic work during the finite-time transition between two NESS. We compare optimal protocols in viscous and viscoelastic fluid environments, which are common in realistic technical and biological processes and introduce memory due to a delayed response. Regardless of the presence of memory effects, optimal protocols consistently balance energy extraction with dissipation minimization. In the presence of memory, optimal control is achieved if the protocol matches the time response of the environment. These findings offer key insights for designing optimal control strategies for finite-time, nonequilibrium processes in complex environments.

DOI: 10.1073/pnas.2510654122

Source: https://www.pnas.org/doi/abs/10.1073/pnas.2510654122