Gujrati P D
Department of Physics, Department of Polymer Science, The University of Akron, Akron, Ohio 44325, USA.
Phys Rev E. 2020 Jul;102(1-1):012140. doi: 10.1103/PhysRevE.102.012140.
We present a first-principles thermodynamic approach to provide an alternative to the Langevin equation by identifying the deterministic (no stochastic component) microforce F_{k,BP} acting on a nonequilibrium Brownian particle (BP) in its kth microstate m_{k}. (The prefix "micro" refers to microstate quantities and carry a suffix k.) The deterministic new equation is easier to solve using basic calculus. Being oblivious to the second law, F_{k,BP} does not always oppose motion but viscous dissipation emerges upon ensemble averaging. The equipartition theorem is always satisfied. We reproduce well-known results of the BP in equilibrium. We explain how the microforce is obtained directly from the mutual potential energy of interaction beween the BP and the medium after we average it over the medium so we only have to consider the particles in the BP. Our approach goes beyond the phenomenological and equilibrium approach of Langevin and unifies nonequilibrium viscous dissipation from mesoscopic to macroscopic scales and provides new insight into Brownian motion beyond Langevin's and Einstein's formulation.
我们提出了一种第一性原理热力学方法，通过确定作用于处于其第k个微观状态(m_{k})的非平衡布朗粒子（BP）上的确定性（无随机成分）微观力(F_{k,BP})，为朗之万方程提供一种替代方法。（前缀“微观”指微观状态量，并带有下标k。）这个确定性的新方程使用基本微积分更容易求解。由于忽略了第二定律，(F_{k,BP})并不总是阻碍运动，但在系综平均时会出现粘性耗散。能均分定理总是成立的。我们重现了BP在平衡状态下的著名结果。我们解释了在对介质进行平均后，如何直接从BP与介质之间的相互作用势能中获得微观力，这样我们只需要考虑BP中的粒子。我们的方法超越了朗之万的唯象和平衡方法，统一了从介观到宏观尺度的非平衡粘性耗散，并为超越朗之万和爱因斯坦公式的布朗运动提供了新的见解。
