http://blogs.discovermagazine.com/cosmicvariance/2008/12/29/richard-feynman-on-boltzmann-brains/
分子熱運動粒子數守恆 的結果 (無引號)：
分子熱運動粒子數守恆 的結果 (無引號)：
搜尋結果
分子热运动能量守恒- dsl62389的日志- 网易博客
dsl62389.blog.163.com/blog/.../39564435201052075155... - 轉為繁體網頁2010年6月20日 - （2）阿伏加德罗常数： 分子热运动能量守恒- dsl62389 - dsl62389博客 任何物质含有的粒子数都相同，这个常数叫阿伏加德罗常数。 分子热运动能量 ...[PDF]教案讨论一分子热运动和统计分布 - 复旦大学精品课程
jpkc.fudan.edu.cn/.../48e9b6a7-92ef-4e9e-b698-8898dba...
轉為繁體網頁在经典物理中，单个粒子的运动遵守牛顿力学的规律．若已知 ... 弹性的，动量和动能都是守恒的．在一个 ... 利用此软件可以形象地看出统计规律性：当粒子数N 很少时，按速率的分. 布)( ... 分子热运动和统计分布（复旦大学物理系，孙鑫，2004 年4 月）. 3. 28、“热学”之一'布朗运动与热传递'_论理_新浪博客
blog.sina.com.cn/s/blog_8f874b490100uftz.html
轉為繁體網頁2011年10月29日 - 分子的无规则运动称为热运动,热现象的本质就是分子的热运动”（见《新概念 .... 才能维持电、热转化过程中的“电荷守恒”、“粒子数守恒”和“能量守恒"。2014年研究生招生考试物理学考试大纲_湖南大学物理与微 ...
physics.hnu.cn/plus/view.php?aid=194
轉為繁體網頁气体分子热运动的算术平均速率、方均根速率。玻耳兹曼 ..... 理解波函数的统计解释，态叠加原理，薛定谔方程的引进及其基本性质，粒子流密度和粒子数守恒，定态；[PDF]布朗運動、郎之萬方程式、與布朗動力學
psroc.phys.ntu.edu.tw/bimonth/v27/456.pdf
這種方法解決了直接以牛頓動量守恆方程追蹤系統. 中所有布朗粒子與流體分子軌跡(稱為分子動力學)的困境：懸殊的時間尺度差異(timescales separation)。 .... mζ(dx/dt)與流體分子因熱運動與其碰撞的熱擾動力 .... 由於系統粒子數龐大再加上截然. 高二物理分子热运动能量守恒_免费教案当知网
beike.dangzhi.com/view/27rpy2
轉為繁體網頁第十一章分子热运动能量守恒. 我们通常把 ... 1、阿伏加德罗常数：1mol的任何物质所含的粒子数，即：NA = 6.02×1023 mol－1（精确值为6.0221367×1023 mol－1）.
Cosmic Variance
Richard Feynman on Boltzmann Brains
The Boltzmann Brain paradox is an argument against the idea that the universe around us, with its incredibly low-entropy early conditions and consequential arrow of time, is simply a statistical fluctuation within some eternal system that spends most of its time in thermal equilibrium. You can get a universe like ours that way, but you’re overwhelmingly more likely to get just a single galaxy, or a single planet, or even just a single brain — so the statistical-fluctuation idea seems to be ruled out by experiment. (With potentially profound consequences.)The first invocation of an argument along these lines, as far as I know, came from Sir Arthur Eddington in 1931. But it’s a fairly straightforward argument, once you grant the assumptions (although there remain critics). So I’m sure that any number of people have thought along similar lines, without making a big deal about it.
One of those people, I just noticed, was Richard Feynman. At the end of his chapter on entropy in the Feynman Lectures on Physics, he ponders how to get an arrow of time in a universe governed by time-symmetric underlying laws.
So far as we know, all the fundamental laws of physics, such as Newton’s equations, are reversible. Then were does irreversibility come from? It comes from order going to disorder, but we do not understand this until we know the origin of the order. Why is it that the situations we find ourselves in every day are always out of equilibrium?Feynman, following the same logic as Boltzmann, contemplates the possibility that we’re all just a statistical fluctuation.
One possible explanation is the following. Look again at our box of mixed white and black molecules. Now it is possible, if we wait long enough, by sheer, grossly improbable, but possible, accident, that the distribution of molecules gets to be mostly white on one side and mostly black on the other. After that, as time goes on and accidents continue, they get more mixed up again.But, of course, it doesn’t really suffice as an explanation for the real universe in which we live, for the same reasons that Eddington gave — the Boltzmann Brain argument.
Thus one possible explanation of the high degree of order in the present-day world is that it is just a question of luck. Perhaps our universe happened to have had a fluctuation of some kind in the past, in which things got somewhat separated, and now they are running back together again. This kind of theory is not unsymmetrical, because we can ask what the separated gas looks like either a little in the future or a little in the past. In either case, we see a grey smear at the interface, because the molecules are mixing again. No matter which way we run time, the gas mixes. So this theory would say the irreversibility is just one of the accidents of life.
We would like to argue that this is not the case. Suppose we do not look at the whole box at once, but only at a piece of the box. Then, at a certain moment, suppose we discover a certain amount of order. In this little piece, white and black are separate. What should we deduce about the condition in places where we have not yet looked? If we really believe that the order arose from complete disorder by a fluctuation, we must surely take the most likely fluctuation which could produce it, and the most likely condition is not that the rest of it has also become disentangled! Therefore, from the hypothesis that the world is a fluctuation, all of the predictions are that if we look at a part of the world we have never seen before, we will find it mixed up, and not like the piece we just looked at. If our order were due to a fluctuation, we would not expect order anywhere but where we have just noticed it.After pointing out that we do, in fact, see order (low entropy) in new places all the time, he goes on to emphasize the cosmological origin of the Second Law and the arrow of time:
We therefore conclude that the universe is not a fluctuation, and that the order is a memory of conditions when things started. This is not to say that we understand the logic of it. For some reason, the universe at one time had a very low entropy for its energy content, and since then the entropy has increased. So that is the way toward the future. That is the origin of all irreversibility, that is what makes the processes of growth and decay, that makes us remember the past and not the future, remember the things which are closer to that moment in history of the universe when the order was higher than now, and why we are not able to remember things where the disorder is higher than now, which we call the future.And he closes by noting that our understanding of the early universe will have to improve before we can answer these questions.
This one-wayness is interrelated with the fact that the ratchet [a model irreversible system discussed earlier in the chapter] is part of the universe. It is part of the universe not only in the sense that it obeys the physical laws of the universe, but its one-way behavior is tied to the one-way behavior of the entire universe. It cannot be completely understood until the mystery of the beginnings of the history of the universe are reduced still further from speculation to scientific understanding.We’re still working on that.
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