电流变效应的研究

电流变效应的研究(中文6000字,英文4000字)
附录 I  译文
              (29)
这个值是最大限度地相对于一个过渡概率 的最小化。对于Δt，而不是相对于目标值 的最小化A，同样是通过最小化达到相对率  。事实上，对右边等式（29）进行简单的最小化，就得到力平衡方程
                                 (30)
即，朗之万方程没有随机力。这是合理的，因为随机力为零意味着式（30）是真实的平均值。
因此，我们从上可得:
（一）    可以有一个变分泛函，其数量是一个变量，这是相对率的最小化；
（二）    这样的结果会保证最小平均力的平衡；
（三）    同时最小化所产生的运动方程及相关边界条件，代表了最有可能的耗散过程。
最后声明基本上保证了在统计意义上，最有可能的动态过程的宏观观察。对于多变量的一般情况，可以简单地概括为式（29）
 ，             （31）
在人工智能的场变量 的情况下，应改为积分的总和，通过功能性衍生物的偏导数。在式（31）耗散系数矩阵元素的国家司法研究所必须的两项指标的交换对称，如图所示的昂萨格[29,30]基于微观可逆性。

附录II  英文原文
              (29)
is the quantity to be minimized if we want to maximize the probability of transition with respect to  . For a small Δt , it is seen that instead of minimizing A with respect to the target state  , the same is achieved by minimizing with respect to the rate   . Indeed,if we carry out the simple minimization on the right hand side of Eq. (29), we obtain the force balance equation
                              (30)
i.e., the Langevin equation without the stochastic force term. Thisis reasonable, since the stochastic force has a zero mean, so Eq. (30) is true on average.
Thus we learn from the above that
(a) there can be a variational functional, of which the quantity A is the one-variable version, which should be minimized with respect to the rates;
(b) the result of such minimization would guarantee the force balance on average; and
(c) the minimization would also yield the equations of motion and the related boundary conditions, which represent the most probable course of a dissipative process.
   The last statement essentially guarantees that in the statistical sense, the most probable course will be the only dynamic course of action observed macroscopically. For the general case of multivariables, the variational functional can be simply generalized from Eq. (29) as