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assignmentutor-lab™ 为您的留学生涯保驾护航 在代写信息论information theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写信息论information theory代写方面经验极为丰富，各种代写信息论information theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

数学代写|信息论作业代写information theory代考|Maxwell’s demon

In England, the brilliant Scottish theoretical physicist, James Clerk Maxwell (1831-1879) invented a thought experiment which demonstrated that the second law of thermodynamics is statistical in nature and that there is a relationship between entropy and information. It should be mentioned that at the time when Clausius and Maxwell were living, not all scientists agreed about the nature of heat, but Maxwell, like Kelvin, believed heat to be due to the rapid motions of atoms or molecules. The more rapid the motion, the greater the temperature.

In a discussion of the ideas of Carnot and Clausius, Maxwell introduced a model system consisting of a gas-filled box divided into two parts by a wall; and in this wall, Maxwell imagined a small weightless door operated by a “demon”. Initially, Maxwell let the temperature and pressure in both $\mathrm{~ p a r t s ~ o f ~ t h e ̉ ~ b o ̄ x ~ b e ̉ ~ e ́ q u a l . ~ H o w e v e r , ~ h e ̄ ~ m a ̉ d e ~ h i s ~ d e m o n o n ~ o p e r a ̀ a e ~ t h e}$ in such a way as to sort the gas particles: Whenever a rapidly-moving particle approaches from the left, Maxwell’s demon opens the door; but when a slowly moving particle approaches from the left, the demon closes it. The demon has the opposite policy for particles approaching from the right, allowing the slow particles to pass, but turning back the fast ones. At the end of Maxwell’s thought experiment, the particles are sorted, with the slow ones to the left of the barrier, and the fast ones to the right. Although initially, the temperature was uniform throughout the box, at the end a temperature difference has been established, the entropy of the total system is decreased and the second law of thermodynamics is violated.
In 1871 , Maxwell expressed these ideas in the following words: “If we conceive of a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are still finite as our own, would be able to do what is at present impossible to us. For we have seen that the molecules in a vessel full of air are moving at velocities by no means uniform… Now let us suppose that such a vessel full of air at a uniform temperature is divided into two portions, $A$ and $B$, by a division in which there is a small hole, and that a being who can see individual molecules, opens and closes swifter molecules to pass from $\mathrm{A}$ to $\mathrm{B}$, and only slowerr onés to påss from $\mathrm{B}$ to $\mathrm{A}$. Hẽ will thus, withoüt thẽ expenditurẽ of work, raise the temperature of $B$ and lower that of $A$, in contradiction to the second law of thermodynamics.” Of course Maxwell admitted that demons and weightless doors do not exist. However, he pointed out, one could certainly imagine a small hole in the partition between the two halves of the box. The sorting could happen by chance (although the probability of its happening decreases rapidly as the number of gas particles becomes large). By this argument, Maxwell demonstrated that the second law of thermodynamics is a statistical law.

数学代写|信息论作业代写information theory代考|Statistical mechanics

Besides inventing an interesting demon (and besides his monumental contributions to electromagnetic theory), Maxwell also helped to lay the foundations of statistical mechanics. In this enterprise, he was joined by the Austrian physicist Ludwig Boltzmann (1844-1906) and by an American, Josiah Willard Gibbs, whom we will discuss later. Maxwell and Boltzmann worked independently and reached similar conclusions, for which they share the credit. Like Maxwell, Boltzmann also interpreted an increase in entropy as an increase in disorder; and like Maxwell he was a firm believer in atomism at a time when this belief was by no means universal. For example, Ostwald and Mach, both important figure in German science at that time, refused to believe in the existence of atoms, in spite of the fact that Dalton’s atomic ideas had proved to be so useful in chemistry. Towards the end of his life, Boltzmann suffered from periods of severe depression, perhaps because of attacks on his scientific work by Ostwald and others. In 1906 , while on vacation near Trieste, he committed suicide – ironically, just a year before the French physicist J.B. Perrin produced irrefutable evidence of the existence of atoms.

Maxwell and Boltzmann made use of the concept of “phase space”, a $6 N$-dimensional space whose coordinates are the position and momentum coordinates of each of $N$ particles. However, in discussing statistical me-chanics we will use a more modern point of view, the point of view of quantum theory, according to which a system may be in one or another of a set of discrete states, $i=1,2,3, \ldots$ with energies $\epsilon_{i}$.

数学代写|信息论作业代写information theory代考|Maxwell’s demon

1871 年，麦克斯韦用以下的话表达了这些想法：“如果我们设想一个人的能力如此敏锐，以至于他可以跟踪每个分子的运行过程，那么这样一个人，其属性仍然像我们自己一样有限，将能够去做我们目前不可能做的事情。因为我们已经看到，在充满空气的容器中，分子的运动速度绝不是均匀的……现在让我们假设这样一个充满均匀温度的空气的容器被分成两部分，一个和乙, 通过一个有一个小洞的划分, 一个可以看到单个分子的存在, 打开和关闭更快的分子从一个至乙，并且只有较慢的人可以通过乙至一个. Hẽ 将因此，无需 thẽ 工作支出，提高温度乙并降低一个，与热力学第二定律相矛盾。” 当然，麦克斯韦承认恶魔和失重门并不存在。然而，他指出，人们当然可以想象盒子两半之间的隔板上有一个小洞。排序可能是偶然发生的（尽管随着气体粒子的数量变大，它发生的概率会迅速降低）。通过这个论点，麦克斯韦证明了热力学第二定律是一个统计定律。

有限元方法代写

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MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

assignmentutor™您的专属作业导师
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