2022年7月10日 · Given the partition function Z Z of a (finite size) system, the free energy is given by F = −kT log[Z] F = − k T log. [Z], where k k is the Boltzmann constant. (for example the Ising model with N N particles). But when we take the thermodynamic limit, it becomes. limN→∞ − 1 Nlog[ZN], lim N → ∞ − 1 N log [Z N], with N N the amount of particles.

The real part of log (z) is the natural logarithm of |z|. Its graph is thus obtained by rotating the graph of ln (x) around the z -axis. In mathematics, a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers. The term refers to one of the following, which are strongly related:

Our goal in this section is to define the log function. We want log(z) to be the inverse of ez. That is, we want elog (z) = z. We will see that log(z) is multiple-valued, so when we use it we will have to specify a branch. We start by looking at the simplest example which illustrates that log(z) is …

e) There is no energy gap behavior because there is no gap in the classically allowed rotational energies. The quantum result, however, will show an energy gap. Problem 2: Adsorption On a Stepped Surface a) Z1 = P states exp( state =kT ) = 0:01M …

该指数形式实际上来自于选取 约束内最均匀 的分布的“必经之路”——最大化香农熵。 而香农熵的形式自然包含对指数族的偏爱。 已写成专栏文章，内详： 这个问题有绕开系综的答案。 去年在一位学经济的朋友那里蹭饭，顺道听了一位做经济物理的老师给的一个关于收入分布的报告，之后朋友问了一个几乎一样的问题——物理里面那些exp是哪来的。 这个回答算是给做经济的朋友的一个回复，理解起来只需要一点高中数学的底子（+sterling公式）。 问题实际上有两层：首先定性 …

前几天在一道题上看到，光子E=kT，k是玻尔兹曼常数 觉得很奇怪，用理想气体可以推出E=n/2·kT n是自由度。 如果这样来看那光子的自由度是2，感觉…

2018年11月1日 · with k = log(1 + z) k = log (1 + z). Is it possible the answer is from the logistic growth formula? If so, how would one proceed to get the answer from there? @int0194 it seems that simply k = ln(1 + z) k = ln (1 + z) is a given expression to determine the parameter k k as a function of teh other parameter z z.

我们把 Z (z, V, T) 叫做 巨分配函数。 由定义，体积 V 里的平均分子数量 \overline {N} 为 \overline {N} \equiv \langle N \rangle = \frac {\displaystyle\sum_ {N=0}^ {\infty}Nz^nQ_N (V, T)} {\displaystyle\sum_ {N=0}^ {\infty}z^NQ (V, T)} = z\frac {\partial } {\partial z}\log Z (z, V, T)\\

Some statistical physics book use: $Z=\sum e^ {-H}$ and $F=-\ln Z$ as definition for partition function and free energy. I think they should be $Z=\sum e^ {-\frac {H} {kT}}$ and $F=-kT \ln Z$ Are they

例2.2试求单位阶跃时间序列y (kT)=u (kT)的z变换. =1+z-1+z-2+z-3+… (等比数列求和) 例2.3试求衰减指数序列y (kT)= e-akT的Z变换Y (z)。 =1+ e-aTz-1+e-2aTz-2+e-3aTz-3+…