We present a to provide an alternative to the Langevin equation by identifying the (no stochastic component) microforce ${𝐅}_{k,\mathrm{\text{BP}}}$ acting on a nonequilibrium Brownian particle (BP) in its $k$th 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, ${𝐅}_{k,\mathrm{\text{BP}}}$ does 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.

中文翻译：

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布朗粒子和微观粘性阻力的第一性原理非平衡确定性方程

我们提出了一种方法，通过识别（无随机分量）微力来提供Langevin方程的替代方案 ${𝐅}_{ķ，\mathrm{\text{血压}}}$ 作用于非平衡布朗粒子（BP） $ķ$微观状态 ${𝔪}_{ķ}$。（前缀微是指微状态数量，并带有后缀$ķ$。）使用基本演算更容易解决确定性新方程式。由于不遵守第二定律，${𝐅}_{ķ，\mathrm{\text{血压}}}$确实总是反对运动，但在合奏平均时会出现粘性耗散。等分定理总是满足的。我们重现了BP平衡的众所周知的结果。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的互有势能直接获得微力，因此我们只需要考虑BP中的颗粒即可。我们的方法超越了Langevin的现象学和平衡方法，并统一了从介观尺度到宏观尺度的非平衡粘性耗散，并为Langevin和Einstein公式之外的布朗运动提供了新的见解。