今天终于拿到了加工的表面张力测量设备。虽然在设计的时候，选的是自由公差，装配起来稍微有点难看，但基本上应该管用。
在学校的工程实践中心，看到了很多“新”玩意儿，也看了线切割过程。现在的技术真是先进啊。几天不关心就发现落伍了。今后再复杂的构件都能随意加工了。贴一个百度的特种加工技术介绍，将来都尝试一下。
特种加工
目录
特种加工的主要运用领域 激光加工技术 电子束加工技术 离子束及等离子体加工技术 电加工技术 特种加工发展方向及研究
特种加工亦称“非传统加工”或“现代加工方法”，泛指用电能、热能、光能、电化学能、化学能、声能及特殊机械能等能量达到去除或增加材料的加工方法，从而实现材料被去除、变形 、改变性能或被镀覆等。
与传统机械加工方法相比具有许多独到之处：
(1)加工范围不受材料物理 、机械性能的限制，能加工任何硬的、软的、脆的、耐热或高熔点金属以及非金属材料。
(2)易于加工复杂型面、微细表面以及柔性零件。
(3)易获得 良好的表面质量，热应力、残余应力、冷作硬化、热影响区等均比较小。
(4)各种加工方法易复合形成新工艺方法，便于推广应用。
特种加工的主要运用领域
特种加工技术在国际上被称为21世纪的技术，对新型武器装备的研制和生产，起到举足轻重的作用。随着新型武器装备的发展，国内外对特种加工技术的需求日益迫切。不论飞机、导弹，还是其它作战平台都要求降低结构重量，提高飞行速度，增大航程，降低燃油消耗，达到战技性能高、结构寿命长、经济可承受性好。为此，上述武器系统和作战平台都要求采用整体结构、轻量化结构、先进冷却结构等新型结构，以及
钛合金、
复合材料、粉末材料、金属间化合物等新材料。
为此，需要采用特种加工技术，以解决武器装备制造中用常规加工方法无法实现的加工难题，所以特种加工技术的主要应用领域是：
难加工材料，如钛合金、耐热不锈钢、高强钢、复合材料、工程陶瓷、金刚石、红宝石、硬化玻璃等高硬度、高韧性、高强度、高熔点材料。
难加工零件，如复杂零件三维型腔、型孔、群孔和窄缝等的加工。
低刚度零件，如薄壁零件、弹性元件等零件的加工。
以高能量密度束流实现焊接、切割、制孔、喷涂、表面改性、刻蚀和精细加工。
激光加工技术
国外激光加工设备和工艺发展迅速，现已拥有100kW的大功率CO2激光器、kW级高光束质量的Nd:YAG固体激光器，有的可配上光导纤维进行多工位、远距离工作。激光加工设备功率大、自动化程度高，已普遍采用CNC控制、多坐标联动，并装有激光功率监控、自动聚焦、工业电视显示等辅助系统。
激光制孔的最小孔径已达0.002mm，已成功地应用自动化六坐标激光制孔专用设备加工航空发动机涡轮叶片、燃烧室气膜孔，达到无再铸层、无微裂纹的效果。激光切割适用于由耐热合金、钛合金、复合材料制成的零件。目前薄材切割速度可达15m/min，切缝窄，一般在0.1～1mm之间，热影响区只有切缝宽的10%～20%，最大切割厚度可达45mm，已广泛应用于飞机三维蒙皮、框架、舰船船身板架、直升机旋翼、发动机燃烧室等。
激光焊接薄板已相当普遍，大部分用于汽车工业、宇航和仪表工业。激光精微焊接技术已成为航空电子设备、高精密机械设备中微型件封装结点的微型连接的重要手段。激光表面强化、表面重熔、合金化、非晶化处理技术应用越来越广，激光微细加工在电子、生物、医疗工程方面的应用已成为无可替代的特种加工技术。激光快速成型技术已从研究开发阶段发展到实际应用阶段，已显示出广阔的应用前景。
国内70年代初已开始进行激光加工的应用研究，但发展速度缓慢。在激光制孔、激光热处理、焊接等方面虽有一定的应用，但质量不稳定。目前已研制出具有光纤传输的固体激光加工系统，并实现光纤耦合三光束的同步焊接和石英表芯的激光焊接。完成了激光烧结快速成型原理样机研制，并采用环氧聚脂和树脂砂烧结粉末材料，快速成型出典型零件，如叶轮、齿轮。
激光加工技术今后几年应结合已取得的预研成果，针对需求，重点开展无缺陷气膜小孔的激光加工及实时检控技术、高强铝(含铝锂、铝镁)合金的激光焊接技术、金属零件的激光粉末烧结快速成型技术、激光精密加工及重要构件的激光冲击强化等项目的研究。实现高温涡轮发动机气膜孔无缺陷加工，可使叶片使用寿命达2000小时以上；以焊代替数控加工飞机次承力构件，以及带筋壁板的以焊代铆；实现重要零部件的表面强化，提高安全性、可靠性等，从而使先进的激光制造技术在军事工业中发挥更大的作用。
电子束加工技术
电子束加工技术在国际上日趋成熟，应用范围广。国外定型生产的40kV～300kV的电子枪(以60kV、150kV为主)，已普遍采用CNC控制，多坐标联动，自动化程度高。电子束焊接已成功地应用在特种材料、异种材料、空间复杂曲线、变截面焊接等方面。目前正在研究焊缝自动跟踪、填丝焊接、非真空焊接等，最大焊接熔深可达300mm，焊缝深宽比20：1。电子束焊已用于运载火箭、航天飞机等主承力构件大型结构的组合焊接，以及飞机梁、框、起落架部件、发动机整体转子、机匣、功率轴等重要结构件和核动力装置压力容器的制造。如：F-22战斗机采用先进的电子束焊接，减轻了飞机重量，提高了整机的性能；“苏-27”及其它系列飞机中的大量承力构件，如起落架、承力隔框等，均采用了高压电子束焊接技术。
国内多种型号的飞机及发动机和多种型号的导弹壳体、油箱、尾喷管等结构件均已采用了电子束焊接。因此，电子束焊接技术的应用越来越广泛，对电子束焊接设备的需求量也越来越大。
国外的电子束焊机，以德国、美国、法国、乌克兰等为代表，已达到了工程化生产。其特点是采用变频电源，设备的体积、噪声、高压性能等方面都有很大提高；在控制系统方面，运用了先进的计算机技术，采用了先进的CNC及PLC技术，使设备的控制更可靠，操作更简便、直观。
国外真空电子束物理气相沉积技术，已用于航空发动机涡轮叶片高温防腐隔热陶瓷涂层，提高了涂层的抗热冲击性能及寿命。电子束刻蚀、电子束辐照固化树脂基复合材料技术正处于研究阶段。
电子束加工技术今后应积极拓展专业领域，紧密跟踪国际先进技术的发展，针对需求，重点开展电子束物理气相沉积关键技术研究、主承力结构件电子束焊接研究、电子束辐照固化技术研究、电子束焊机关键技术研究等。
离子束及等离子体加工技术
表面功能涂层具有高硬度、耐磨、抗蚀功能，可显著提高零件的寿命，在工业上具有广泛用途。美国及欧洲国家目前多数用微波ECR等离子体源来制备各种功能涂层。等离子体热喷涂技术已经进入工程化应用，已广泛应用在航空、航天、船舶等领域的产品关键零部件耐磨涂层、封严涂层、热障涂层和高温防护层等方面。
等离子焊接已成功应用于18mm铝合金的储箱焊接。配有机器人和焊缝跟踪系统的等离子体焊在空间复杂焊缝的焊接也已实用化。微束等离子体焊在精密零部件的焊接中应用广泛。我国等离子体喷涂已应用于武器装备的研制，主要用于耐磨涂层、封严涂层、热障涂层和高温防护涂层等。
真空等离子体喷涂技术和全方位离子注入技术已开始研究，与国外尚有较大差距。等离子体焊接在生产中虽有应用，但焊接质量不稳定。离子束及等离子体加工技术今后应结合已取得的成果，针对需求，重点开展热障涂层及离子注入表面改性的新技术研究，同时，在已取得初步成果的基础上，进一步开展等离子体焊接技术研究。
电加工技术
国外电解加工应用较广，除叶片和整体叶轮外已扩大到机匣、盘环零件和深小孔加工，用电解加工可加工出高精度金属反射镜面。目前电解加工机床最大容量已达到5万安培，并已实现CNC控制和多参数自适应控制。电火花加工气膜孔采用多通道、纳秒级超高频脉冲电源和多电极同时加工的专用设备，加工效率2～3秒/孔，表面粗糙度Ra0.4μm，通用高档电火花成型及线切割已能提供微米级加工精度，可加工3μm的微细轴和5μm的孔。精密脉冲电解技术已达10μm左右。电解与电火花复合加工，电解磨削、电火花磨削已用于生产。
特种加工发展方向及研究
根据上述现状，今后特种加工技术的发展方向应是：
(1)不断改进、提高高能束源品质，并向大功率、高可靠性方向发展。
(2)高能束流加工设备向多功能、精密化和智能化方向发展，力求达到标准化、系列化和模块化的目的。扩大应用范围，向复合加工方向发展。
(3)不断推进高能束流加工新技术、新工艺、新设备的工程化和产业化工作。
为实现以上发展目标，必须开展下列加工工艺的技术研究：
(1)激光加工技术
无再铸层、无微裂纹涡轮叶片气膜孔激光高效加工技术研究；
铝合金、超强钢、钛合金、异种材料构件以及大型空间曲面零件的激光焊接工艺研究；
三维激光切割工艺规范及表面质量控制技术和在线测量控制技术研究；
提高高温合金、铝合金等重要部件抗疲劳性能的激光冲击技术研究；
激光快速成型技术研究；
大功率激光熔覆陶瓷涂层的工艺以及涂层组织结构和性能的研究。
(2)电子束加工技术
150kV、15kW高压电子枪及高压电源的技术研究；
电子束物理气相沉积技术的研究；
大厚度变截面钛合金的电子束焊接技术研究及质量评定；
典型复合材料飞机构件的电子束固化工艺研究及其工程化研究；
多功能电子束加工技术研究。
(3)离子束和等离子体加工技术
复杂零件“保形”离子注入与混合沉积技术研究，获得高密度等离子体方法研究；
空间结构焊接工艺参数自适应控制及焊缝自动跟踪系统研究，以及等离子弧焊过程中变形控制技术研究；
等离子喷涂陶瓷热障涂层结构、工艺及工程化研究；
层流湍流自动转换技术及轴向送粉、三维喷涂技术研究；
层流等离子体喷涂系统的研制及其喷涂技术的研究。
(4)电加工技术
高品质深小孔电液束加工技术研究；
高效、优质照相电解加工群孔技术研究；
多轴、多通道电火花加工群孔、异形孔技术研究；
大容量(5000A及以上)精密电解加工技术研究；
电解—电火花复合加工技术研究。
研究上述技术的关键在于：提高高能束流的品质；开展特种加工过程的自动控制及计算机建模、仿真技术的研究；新材料加工特性研究；特种加工设备的研究等。
http://blog.csdn.net/duanbingnan/archive/2007/10/30/1856105.aspx
一、预处理的由来：
在C++的历史发展中，有很多的语言特征（特别是语言的晦涩之处）来自于C语言，预处理就是其中的一个。C++从C语言那里把C语言预处理器继承过来（C语言预处理器，被Bjarne博士简称为Cpp，不知道是不是C Program Preprocessor的简称）。
二、常见的预处理功能：
预处理器的主要作用就是把通过预处理的内建功能对一个资源进行等价替换，最常见的预处理有：文件包含，条件编译、布局控制和宏替换4种。
文件包含：#include 是一种最为常见的预处理，主要是做为文件的引用组合源程序正文。
条件编译：#if,#ifndef,#ifdef,#endif,#undef等也是比较常见的预处理，主要是进行编译时进行有选择的挑选，注释掉一些指定的代码，以达到版本控制、防止对文件重复包含的功能。
布局控制：#progma，这也是我们应用预处理的一个重要方面，主要功能是为编译程序提供非常规的控制流信息。
宏替换： #define，这是最常见的用法，它可以定义符号常量、函数功能、重新命名、字符串的拼接等各种功能。
三、预处理指令：
预处理指令的格式如下：
# directive tokens
#符号应该是这一行的第一个非空字符，一般我们把它放在起始位置。如果指令一行放不下，可以通过\进行控制，例如：
#define Error if(error) exit(1) 等价于
#define Error \
if(error) exit(1)
不过我们为了美化起见，一般都不怎么这么用，更常见的方式如下：
# ifdef __BORLANDC__
if_true<(is_convertible<Value,named_template_param_base>::value)>::
template then<make_named_arg, make_key_value>::type Make;
# else
enum { is_named = is_named_parameter<Value>::value };
typedef typename if_true<(is_named)>::template
then<make_named_arg, make_key_value>::type Make;
# endif
下面我们看一下常见的预处理指令：
#define 宏定义
#undef 未定义宏
#include 文本包含
#ifdef 如果宏被定义就进行编译
#ifndef 如果宏未被定义就进行编译
#endif 结束编译块的控制
#if 表达式非零就对代码进行编译
#else 作为其他预处理的剩余选项进行编译
#elif 这是一种#else和#if的组合选项
#line 改变当前的行数和文件名称
#error 输出一个错误信息
#pragma 为编译程序提供非常规的控制流信息
下面我们对这些预处理进行一一的说明，考虑到宏的重要性和繁琐性，我们把它放到最后讲。
四、文件包含指令：
这种预处理使用方式是最为常见的，平时我们编写程序都会用到，最常见的用法是：
#include <iostream> //标准库头文件
#include <iostream.h> //旧式的标准库头文件
#include "IO.h" //用户自定义的头文件
#include "../file.h" //UNIX下的父目录下的头文件
#include "/usr/local/file.h" //UNIX下的完整路径
#include "..\file.h" //Dos下的父目录下的头文件
#include "\usr\local\file.h" //Dos下的完整路径
这里面有2个地方要注意：
1、我们用<iostream>还是<iostream.h>?
我们主张使用<iostream>，而不是<iostream.h>,为什么呢？我想你可能还记得我曾经给出过几点理由，这里我大致的说一下：首先，.h格式的头文件早在98年9月份就被标准委员会抛弃了，我们应该紧跟标准，以适合时代的发展。其次，iostream.h只支持窄字符集，iostream则支持窄/宽字符集。
还有，标准对iostream作了很多的改动，接口和实现都有了变化。最后，iostream组件全部放入namespace std中，防止了名字污染。
2、<io.h>和"io.h"的区别？
其实他们唯一的区别就是搜索路径不同：
对于#include <io.h> ，编译器从标准库路径开始搜索
对于#include "io.h" ，编译器从用户的工作路径开始搜索
五、编译控制指令：
这些指令的主要目的是进行编译时进行有选择的挑选，注释掉一些指定的代码，以达到版本控制、防止对文件重复包含的功能。
使用格式，如下：
1、
#ifdef identifier
your code
#endif
如果identifier为一个定义了的符号，your code就会被编译，否则剔除
2、
#ifndef identifier
your code
#endif
如果identifier为一个未定义的符号，your code就会被编译，否则剔除
3、
#if expression
your code
#endif
如果expression非零，your code就会被编译，否则剔除
4、
#ifdef identifier
your code1
#else
your code2
#endif
如果identifier为一个定义了的符号，your code1就会被编译，否则yourcode2就会被编译
5、
#if expressin1
your code1
#elif expression2 //呵呵，elif
your code2
#else
your code3
#enif
如果epression1非零，就编译your code1，否则，如果expression2非零，就编译your code2，否则，就编译your code3
其他预编译指令
除了上面我们说的集中常用的编译指令，还有3种不太常见的编译指令：#line、#error、#pragma，我们接下来就简单的谈一下。
#line的语法如下：
#line number filename
例如：#line 30 a.h 其中，文件名a.h可以省略不写。
这条指令可以改变当前的行号和文件名，例如上面的这条预处理指令就可以改变当前的行号为30，文件名是a.h。初看起来似乎没有什么用，不过，他还是有点用的，那就是用在编译器的编写中，我们知道编译器对C++源码编译过程中会产生一些中间文件，通过这条指令，可以保证文件名是固定的，不会被这些中间文件代替，有利于进行分析。
#error语法如下：
#error info
例如：#ifndef UNIX
#error This software requires the UNIX OS.
#endif
这条指令主要是给出错误信息，上面的这个例子就是，如果没有在UNIX环境下，就会输出This software requires the UNIX OS.然后诱发编译器终止。所以总的来说，这条指令的目的就是在程序崩溃之前能够给出一定的信息。
#pragma是非统一的，他要依靠各个编译器生产者，例如，在SUN C++编译器中：
// 把name和val的起始地址调整为8个字节的倍数
#progma align 8 (name, val)
char name[9];
double val;
//在程序执行开始，调用函数MyFunction
#progma init (MyFunction)
预定义标识符
为了处理一些有用的信息，预处理定义了一些预处理标识符，虽然各种编译器的预处理标识符不尽相同，但是他们都会处理下面的4种：
__FILE__ 正在编译的文件的名字
__LINE__ 正在编译的文件的行号
__DATE__ 编译时刻的日期字符串，例如： "25 Dec 2000"
__TIME__ 编译时刻的时间字符串，例如： "12:30:55"
例如：cout<<"The file is :"<<__FILE__"<<"! The lines is:"<<__LINE__<<endl;
预处理何去何从
如何取代#include预处理指令，我们在这里就不再一一讨论了。
C++并没有为#include提供替代形式，但是namespace提供了一种作用域机制，它能以某种方式支持组合，利用它可以改善#include的行为方式，但是我们还是无法取代#include。
#progma应该算是一个可有可无的预处理指令，按照C++之父Bjarne的话说，就是："#progma被过分的经常的用于将语言语义的变形隐藏到编译系统里，或者被用于提供带有特殊语义和笨拙语法的语言扩充。”
对于#ifdef，我们仍然束手无策，就算是我们利用if语句和常量表达式，仍然不足以替代她，因为一个if语句的正文必须在语法上正确，满足类检查，即使他处在一个绝不会被执行的分支里面。
本打算把FLUENT的后台执行功能调通以后，可以远程提交作业，并关闭本地机。搞了半天，发现，原来不能关，一关程序跟着死！
不过总算搞通了BATCH提交作业——可以预先设定计算参数，存在input文件里，而不用不停跟踪程序。
BATCH操作：
BATCH是FLUENT 提供的无图形界面启动功能，它将把FLUENT计算过程产生的文件存储在文件内，为不同线程通过远程登录用户监视计算过程。当前就用了很简单的功能：
;读入数据
rc temp.cas
rd temp.dat
;非定常问题求解
/solve/dual-time-iterate
10
500
;输出
/file/write-case-data fin.cas
exit
yes
一个网站上的例子
rc def.cas
rd def.dat
solve/set/time-step 0.01
solve/set/reporting-interval 20
solve/dual-time-iterate 10
it 100
wd def10.dat
solve/set/time-step 0.01
solve/set/reporting-interval 20
solve/dual-time-iterate 10
it 100
wd def20.dat
solve/set/time-step 0.01
solve/set/reporting-interval 20
solve/dual-time-iterate 10
it 100
wd def30.dat
solve/set/time-step 0.01
solve/set/reporting-interval 20
solve/dual-time-iterate 10
it 100
wd def40.dat
solve/set/time-step 0.01
solve/set/reporting-interval 20
solve/dual-time-iterate 10
it 100
wd def50.dat
solve/set/time-step 0.01
solve/set/reporting-interval 20
solve/dual-time-iterate 10
it 100
wd def60.dat
solve/set/time-step 0.01
solve/set/reporting-interval 20
solve/dual-time-iterate 10
it 100
wd def70.dat
solve/set/time-step 0.01
solve/set/reporting-interval 20
solve/dual-time-iterate 10
it 100
wd def80.dat
solve/set/time-step 0.01
solve/set/reporting-interval 20
solve/dual-time-iterate 10
it 100
wd def90.dat
solve/set/time-step 0.01
solve/set/reporting-interval 20
solve/dual-time-iterate 10
it 100
wd def100.dat
exit
From: http://lcni.uoregon.edu/~mark/Stat_mech/thermodynamic_entropy_and_information.html
The connection between thermodynamic entropy and information
The bottom line is that thermodynamic entropy is best understood not as a property or macroscopic state of matter (like mass, temperature, or pressure), but as a lack of knowledge of the detailed configuration of matter. In particular, thermodynamic entropy is a measure of our lack of information about the microstate of a closed system of matter near equilibrium. To make this concrete, I'll compare two similar simple systems, one of particles and one of bits. Although the concept of entropy in classical thermodynamics was elucidated long before information theory was developed, thermodynamic entropy can be viewed as a straight-forward application of information theory to a physical problem.
There are many other fine discussions of this topic, but few that strip it down to a simple example. A more in-depth, but more technical, discussion of the same topic is at Entropy in thermodynamics and information theory. But this discussion, and others have the same bottom line, with only a variation of language:
"....it should be remembered that Gibb's statistical mechanical entropy is only one application of information theory to physical systems, relevant when the particular 'message' not yet communicated is the underlying microstate of the physical system."
The 'message' in thermodynamics, the microstate of a physical system, will never be communicated as it is inaccessible to observation or transmission. A good diagram illustrating this idea of "physical information" is in M. P. Franks paper "Physical limits of Computing".
Consider a perfectly insulated 2-D box of simple particles. The
macrostate of an ideal gas can be specified by the total energy E, number of particles N and volume V. There are a large but finite number of possible microstates that are all consistent with this system's single, and unchanging, macro-state:
Ludwig Boltzmann's leap of imagination was that the number of possible microstates, Ω, was finite, and in some sense a particle's state is discrete. But it wasn't until quantum mechanics was developed that this was clarified and shown to be strictly true.
Henri Poincairé and others showed that such an ideal particle system would necessarily cycle through all possible microstates, and that each would be visited with equal probability. The same holds for all practical purposes in real physical systems; no state or group of states is favored.
|
Any one of these microstate is equally likely to be the actual microstate (near equilibrium) and we have no way of knowing which is the actual microstate. And we never will. This lack of information is not because we haven't examined the system closely; it reflects the inaccessibility of this information near equilibrium. But we
can count how many microstates are possible.
The thermodynamic entropy,
S, for this case is:
S/k = log(Ωp) Ωp = number of equally probable microstates, k = Boltzmann's constant
Boltzmann's form of this equation is S = k ln(Ωp), where Boltzmann's constant has SI units of JK-1. Because thermodynamic entropy is dependent on the energy and temperature of of the system, it was convenient to use this proportionality constant if these variables are measured or derived.
An alternative, used here, is to normalize thermodynamic variables such that the proportionallity constant is defined as 1. From Entropy in thermodynamics and information theory:
"The presence of Boltzmann's constant k in the thermodynamic definitions is a historical accident, reflecting the conventional units of temperature. It is there to make sure that the statistical definition of thermodynamic entropy matches the classical entropy of Clausius, thermodynamically conjugate to temperature. For a simple compressible system that can only perform volume work, the first law of thermodynamics becomes
But one can equally well write this equation in terms of what physicists and chemists sometimes call the 'reduced' or dimensionless entropy, σ = S/k, so that
Just as S is conjugate to T, so σ is conjugate to kT (the energy that is characteristic of T on a molecular scale)."
Writing the equation in this way doesn't change thermodynamics, or its expression in information theoretic terms.
|
This statistical measure of thermodynamic entropy quantifies the uncertainty about which microstate is occupied. The higher the number of equally probable possibilities, the more uncertainty. Near equilibrium the system has a maximum entropy, because there are the most possible microstates near equilibrium. For example, there are very few possibilities for all the particles clumped in one corner of our insulated box but many possible ways they can be roughly evenly distributed across the box.
Compare this with a set of 2-D 4 x 4 arrays of bits (images in this case, each one a kind of message), each with the same macro-state specified by the number of bits (N = 16, represented by black or white squares). Note that the number of bits, N, is the same in each instance, although all combinations of black and white are in the set. If an acquaintance is to send you an image/message of this form (a 16-bit email, for example), and you have no prior information about which image/message is to be sent, then each of a
countable number (65,536) of images/messages is equally probable.
The information theory entropy (Shannon entropy), H, for this case is defined as:
H = log(Ωp) , Ωp = number of equally probable microstates
The entropy H quantifies the uncertainty about what message is to be received. The higher the number of equally probable possibilities, the more entropy. The image/message has a maximum of entropy before it is received. But after it is received and read, there is no longer any uncertainty; there is only one possible microstate, the image/message itself; Ωp = 1 and H = 0.
If a single one of these arrays is received as an image/message, the information, I, contained in the image/message is:
I = -log(1/Ωs) = log(Ωs) , Ωs = number of equally probable microstates consistent with the message macro-state
If the microstates are not equally probable, these formulas for S, H and I need to be modified. They become weighted sums over all possible states, where the probability of each state is the weighting factor. See Entropy in thermodynamics and information theory.
|
The probability of this particular image/message being sent is 1/Ω
s. The larger the number of possibilities, the more uncertainty is resolved, or entropy reduced, when the particular image/message is received. Information is a measure of how much an image/message (an observed microstate) tells us, by comparison with the number of other messages it could have been (those consistent with the image/message's macrostate).
| Here's the math. For this 16 bit message with 65,536 possibilities, a single message contains I = -log2(1/65,536) bits = -log2(2-16 ) bits = 16 bits. This is the amount the message was "surprising", or how much our uncertainty (entropy) was reduced -- it could have been a lot of things but it was this singular message. But this result -- 16 bits of information is contained in the message -- is not surprising for this simple example; we knew we were to be sent 16 bits and when we received the message we found out what each of the 16 bits was. |
H and
I might seem redundant because the formulas are similar. But
H does
not equal
I. Entropy refers to the uncertainty of an unknown message, and information refers to the probability of a known message occurring by chance alone.
| More accurately, entropy is a measure of uncertainty due to the unknown part of a message/particle system, and information is a measure of reduction of uncertainty due to the known part of a message/particle system. |
Information gained is equal to entropy lost. Information and entropy are two sides of the same probabilistic coin. While a flipped coin is spinning in the air the entropy
H is one bit (an unknown heads or tails), and the information
I is zero. When it lands and is observed, the entropy
H is zero, and the information
I is one bit (a known heads or tails).
S and
H (thermodynamic and Shannon entropy)
are equivalent, in that
S is directly proportional to
H, and this is because the same conditions hold for both systems.
S is reserved for thermodynamics, but
H can can be applied to any statistical system. As Shannon and Weaver wrote:
“...the quantity which uniquely meets the natural requirements that one sets up for ‘information’ ... turns out to be exactly that which is known in thermodynamics as entropy.”
The entropy S is a state function of a thermodynamic system, but it can't be directly measured like pressure and temperature (see measuring entropy). There is no entropy-meter; entropy must be infered by varying the state of a system near equlibrium and observing how other thermodynamic variables (pressure, temperature, etc.) respond. This is one reason why the statistical mechanics interpretation of entropy is so important:
"[The] ability to make macroscopic predictions based on microscopic properties is the main asset of statistical mechanics over
thermodynamics. Both theories are governed by the
second law of thermodynamics through the medium of
entropy. However, entropy in thermodynamics can only be known empirically, whereas in statistical mechanics, it is a function of the distribution of the system on its microstates." (from
statistical mechanics)
It might seem like this statistical interpretation of matter can cause matter to be "influenced" by our knowledge, or lack of knowledge, of its microstates. What does information or knowledge about microstates have to do with how a steam engine works! But this train of thought is a result of a misperception of microscopic states in nature. Which microstate a particle system is in is irreducibly (inherently) uncertain, in same sense that the position and momentum of individual particles are uncertain (Heisenberg's uncertainty principle). The fact that entropy almost always increases or stays the same (the second law of thermodynamics) is a statistical statement about the uncertainty of a particle system's microstate.
| The fact that entropy sometimes can and does decrease is often glossed over in discussions of, and even the statement of, the second law of thermodynamics. The usefulness of the second law (it's explanatory power) is due to how frequently entropy doesn't measureably increase for any large number of particles. For even small macroscopic systems with a small number of possible states (e.g. > 1,000 particles each with >10 possible states and >101,000 total possible states), it is highly improbable (p <<< 1/2) that a measureable increase of entropy (e.g. a fractional increase of 1/1,000) will occur in the (current) lifetime of the universe (~1010 years). Almost is good enough for physics too. |
James Clerk Maxwell's thought experiment
Maxwell's demon is an example of the importance of observability/uncertainty in discussing the second law. The experiment's resolution, that the demon
can't cheat the second law because she can't observe the microstate without altering it, highlights the importance of observability/uncertainty in physics.
[To Do: Show how these ideas can be extended to easily percieved messages, particulary images.]
53,754 bit (184 x 289) images ( 2
53754 possible images ). Each pixel is represented by one bit, black or white. These three are particular images, not arbitrary selections from all possible 184 x 289 one-bit images :
Low algorithmic complexity
"simple" (one of very few possible low information images)
High "image available energy" (non-random intensity gradient)
Farthest from equilibrium |
Medium algorithmic complexity
"complex" (one of a few possible medium information images)
Medium "image available energy"
Far from equilibrium |
High algorithmic complexity
"random" (one of many possible nearly random images)
Low "image available energy"
Near equilibrium |