Yasuda Kento, Ishimoto Kenta, Komura Shigeyuki
Research Institute for Mathematical Sciences, <a href="https://ror.org/02kpeqv85">Kyoto University</a>, Kyoto 606-8502, Japan.
Wenzhou Institute, <a href="https://ror.org/05qbk4x57">University of Chinese Academy of Sciences</a>, Wenzhou, Zhejiang 325001, China.
Phys Rev E. 2024 Oct;110(4-1):044104. doi: 10.1103/PhysRevE.110.044104.
Onsager's variational principle provides us with a systematic way to derive dynamical equations for various soft matter and active matter. By reformulating the Onsager-Machlup variational principle (OMVP), which is a time-global principle, we propose a new method to incorporate thermal fluctuations. To demonstrate the utility of the statistical formulation of OMVP, we obtain the diffusion constant of a Brownian particle embedded in a viscous fluid by maximizing the modified Onsager-Machlup integral for the surrounding fluid. We also apply our formulation to a Brownian particle in a steady shear flow, which is a typical nonequilibrium system. Possible extensions of our formulation to internally driven active systems are also discussed.
昂萨格变分原理为我们提供了一种系统的方法来推导各种软物质和活性物质的动力学方程。通过重新表述作为时间全局原理的昂萨格 - 马赫卢普变分原理（OMVP），我们提出了一种纳入热涨落的新方法。为了证明OMVP统计表述的实用性，我们通过最大化周围流体的修正昂萨格 - 马赫卢普积分，得到了嵌入粘性流体中的布朗粒子的扩散常数。我们还将我们的表述应用于稳定剪切流中的布朗粒子，这是一个典型的非平衡系统。我们还讨论了将我们的表述扩展到内部驱动活性系统的可能性。
