ADM-201 dump PMP dumps pdf SSCP exam materials CBAP exam sample questions

人类对“熵”的误解 – 译学馆
未登陆,请登陆后再发表信息
最新评论 (0)
播放视频

人类对“熵”的误解

The Misunderstood Nature of Entropy | Space Time

PBS太空
[MUSIC PLAYING]
感谢brilliant.org对PBS数码工作室的支持
Thank you to brilliant.org for supporting PBS Digital Studios.
熵和热力学第二定律定义了时间之箭
Entropy and the second law of thermodynamics have been credited with defining the arrow of time,
推论出了宇宙大热寂
predicting the ultimateheat death of the universe,
并为结构的发展和衰退提供驱动力
and providing the driving force for the development of structure as well as decay
同时也成为你房间混乱的托辞
and also excusing the messiness of your room.
但是“熵”到底是什么
But what is entropy really,
它对我们的宇宙究竟有多重要呢?
and how fundamental is it to our universe?
[音乐]
[MUSIC PLAYING]
PBS太空
熵绝对是物理学界最有趣
Entropy is surely one of the most intriguing
同时也是被误解最深的一个概念
and misunderstood conceptsin all of physics.
世界是熵增的
The entropy of the universe must always increase,
这是由热力学第二定律所得
so says the second law of thermodynamics.
熵增看似是从更深奥的定理中推演出来的
It’s a law that seemsemergent from deeper laws.
它本质上体现的是统计学的原理
It’s statistical in nature, and yet,
但和其他物理定律相比更重要 更不可避免
may ultimately be more fundamental and unavoidable than any other law in physics.
爱因斯坦曾说
Einstein said that
“……我深信热力学第二定律”
“…the thermodynamics that encapsulates the second law
“是唯一永远不会被推翻的宇宙物理理论……”
is the only physical theory of universal content which I am convinced will never be overthrown…”
伟大的天体物理学家 亚瑟·爱丁顿曾警告说
And the great astrophysicistSir Arthur Eddington warned,
“如果你的理论被发现违背了热力学第二定律”
“If your theory is found to be against the secondlaw of thermodynamics,
“我敢说你没有指望了”
I can give you no hope.
“你的理论必将在极度的羞辱中轰然崩塌”
There is nothing forit but to collapse in deepest humiliation.”
我们对熵有了初步了解
We’ve looked at entropy in the past,
但现在是时候更深入地解开这个大谜团了
but it’s time to go much deeper to unravel the great unraveler.
在接下来几集中
Over some upcoming episodes,
我们将探索熵的不同方面和结果
we’ll explore different aspects and consequences of entropy,
包括它在黑洞热力学中的角色
including its role inblack hole thermodynamics
以及它将如何导致宇宙的终结
and how it will lead tothe end of our universe.
但今天 我们将探讨熵究竟是什么
But today, we’ll see what entropy really is
以及为什么热力学第二定律如此根本 不可避免
and why the second law of thermodynamics is considered to be so fundamental and so unavoidable.
让我们追踪溯源
Let’s start from the beginning.
1824年 萨迪·卡诺出版了《论火的动力》一书
In 1824, Sadi Carnot published his Reflections on the Motive Power of Fire,
他在书中揭示了理想热机效率理论
in which he revealed the theory for perfect engine efficiency.
热机 在卡诺的时代
Heat engines, which in Carnot’s day,
是一种新型蒸汽机
were the new-fangled steam engines,
它通过将热能转化为机械能来工作
worked by turning the flow of heat energy into mechanical energy.
为了让热量流动
For heat to flow,
你需要两个不同温度的热源
you need two reservoirs of different temperature.
一个按照卡诺循环运行的理想热机
A perfectly efficient engine, one undergoing the Carnot cycle,
在热能转移的过程中将不会产生无用功
converts all transferred heat energy into useful work.
理论上 热量和功的转化是可逆的
In principle, that work canthen be converted back into heat
因此两个热源之间又会形成温度差
and so the temperature differential can be restablished.
但是 一个低效的发动机将慢慢地
However, an inefficient engine will slowly
耗尽温度差 降低热流
deplete the difference in temperature, reducing the heat flow,
最终 发动机会熄火
and the engine winds down.
在卡诺之后大约半个世纪
Around a half century after Carnot,
鲁道夫·克劳修斯受其启发
Rudolf Clausius was inspired
量化了这种热能会随时间消耗的趋势
to quantify this tendency of heatenergies to decay over time,
从而引进了“熵”的概念
enter entropy.
克劳修斯将“熵”定义为一种内在属性
Clausius defined entropy as the internal property
当热能在系统内转移时 这一属性将会发生变化
that changes as heat energy moves around within a system.
具体说来 每个系统中熵的变化值
Specifically, the change in entropy of each reservoir
为进出该系统的热能除以其温度
is the heat energy going into or out of that reservoir divided by its temperature.
在卡诺循环中
For a Carnot cycle
熵的总体变化为零
the overall change in entropy is zero
但是在更低效率的循环中
but for any less efficient cycle
熵会增加
entropy increases
事实上 “熵”的增加意味着
In fact, an increase in entropymeans that
热源正在趋向于同一温度
the heat reservoirs are approaching the same temperature
从而降低了做有用功的能力
reducing the capacity to do useful work
卡诺和克劳修斯的研究揭示了
Carnot and Clausius’work revealed entropy
“熵”是一种衡量系统能量的均匀分布情况的指标
as a measure of how evenlyspread out a system’s energy is.
分布得越均匀 能量的用处就越小
The more evenly spread, the less useful the energy is,
而对于孤立系统 最佳状况是
and for an isolated system, the best you can hope for
能量的分离及熵保持恒定
is that the separation of energy and the entropy remain constant.
事实上 熵总是会不断增加的
In reality, it will almost always increase
除非有外部的能量使其重新形成温差
unless energy comes in from the outside to reestablish the temperature differential.
这种对“熵”的理解是从热流的角度来考虑的
This understanding of entropyis in terms of flowing heat,
当时很多科学家 包括卡洛本人
and it came from the days whenmany, including Carnot himself,
都认为热是一种叫做热质的物理流体
believed that heat was aphysical fluid called caloric.
经历了一场革命人们才理解“熵”的本质
It took a revolution to understand the reality of entropy,
那场革命便是统计力学
that revolution was statistical mechanics,
统计力学由伟大的路德维希·玻尔兹曼创立
founded by the great Ludwig Boltzmann
并起源于他的气体运动理论
with his kinetic theory of gases.
该理论将热力学行为解释为
This theory explained thermodynamic behavior
牛顿运动定律下微小粒子个体运动的总和结果
as the summed result of the individual motion of tiny particles under Newton’s laws of motion.
统计力学真的令人震惊
Stat-mech(Statistical mechanics) is really astounding.
竟然是由一个非常简单的想法衍生出来的
It’s founded on an absurdly simple idea.
如果给定一个大规模的可观察量
For a given set of large-scaleobservable properties,
粒子每一种可能的构型都同样有可能出现
every possible configuration of particles that could give those properties is equally likely.
让我们补充一些物理方面的看法
Let’s add some physics speak.
结构上来说
By configuration, I mean the exact arrangement
我们将所有微观粒子的排列 位置 速度等状态
of positions,velocities, et cetera for all microscopic particles.
称之为微观态
We call this the microstate.
我们将大规模宏观特性的特定组合称为宏观态
And we call the specific combination of large-scale macroscopic properties the macrostate.
热力学性质:粒子的温度 压力 体积和数量
Macrostates are entirely definedby thermodynamic properties:
完全定义了宏观态
temperature, pressure, volume,and number of particles.
在一个给定的宏观态中
For a given macrostate,
与这个宏观态热力学性质一致的所有微观态
all microstates consistent with itsthermodynamic properties
是等可能的
are equally likely.
在大多数宏观态下 会存在大量不同的
For some macrostates, there arelots of different microstates
微观形态或者说粒子的排列
or arrangements of particles that lead
这导致了它们具有一些大致等同的热力学性质
to roughly the same thermodynamic properties,
而其他少数的宏观态
while other macrostatescan be produced
仅能由少量微观态形成
by only very few microstates.
好 另一个事实是 如果你让一个系统自行运行
OK. One more fact, if you leave a system to do its own thing,
根据物理定律 最终它会尝试
it’ll eventually try out allpossible microstates that
所有可能的微观态
are possible given the laws of physics.
粒子所有的排列情况最后都会呈现
All particle arrangements will eventually happen.
所以 如果你在随机的时间节点上
So if you look at the system
观测这一系统
at some random point in time,
它将从众多可能的微观态中
it’ll be in a completelyrandom microstate
随机选取一个状态来呈现
chosen from all possible microstates.
那它会变成什么样的宏观态呢?
And what macrostate will it be in?
可能是和微观态最一致的那个宏观态吧
Well, probably the one that’sconsistent with the most microstates.
我们可以对这些微观和宏观状态进行类比思考
We can think of these micro andmacrostates with an analogy.
这是个围棋棋盘
This is a Go board.
假设你随机放置180个黑色棋子
Let’s say you place 180black stones at random.
每一种可能的具体排列都被视为一种微观态
Every possible specific arrangement is considered a microstate,
而分布的整体形状将是宏观态
while the overall shape of the distribution would be the macrostate.
有近2乘10的107次方种方式放置棋子
There are nearly 2 times 10 to the power of 107 ways
其中几乎所有的排列情况都是均匀混杂的
to arrange the pieces and almost all of them are pretty evenly mixed,
因此几乎所有宏观态也都大略相同
so roughly all the same macrostate.
但一些反常的微观态会产生不同的宏观态
Some microstatesare weird though, and they give
different macrostates
因为它们的平均分布不同
because they’re differentaverage distributions.
例如
For example, there’s one
所有的棋子都在一侧的情况
where all of the stones are on one side.
那种微观态及其罕见
That microstate is a factor of
与多数均匀混杂的微观态相比
2 times 10 to the power of 107 less likely
其出现的概率比2乘10的107次方的因数还要小
than one of the many smoothly mixed microstates.
且这个棋盘越大
And the larger the board, the less likely it is
出现这样极端情况的可能性越小
to end up in such a weird arrangement.
若一个房间里含有10的26次方的空气分子
For a room full of 10 to the power of 26 molecules of air,
那么所有的分子随机出现在房间同一侧的可能性
the chance of getting all of the molecules on one side of the room by chance
小到几乎不可能发生
is so small that it never happens.
我们在前面对粒子位置进行了诸多探讨
We’ve been talking a lotabout particle position,
其实那个围棋只是类比了
but really, that Goboard is an analogy
各种属性的所有可能组合
for all possible combinationsof all properties:
这些属性包括位置 动量 旋转 振动
position, momentum, spin, vibration,
以及系统可以拥有的任何自由度
really any “degree of freedom”that the system can have.
我们将系统所有可能状态的空间称为相空间
We call this space ofproperties a phase space.
而且 微观态并非取决于粒子在位置空间中的分布
And instead of particles beingdistributed through position space,
它实则是由相空间中的能量分布来决定的
a microstateis really defined by how energy is distributed
through phase space.
每个粒子在相空间中的平均分布
The average distributionof individual particles in phase space
决定了这个系统的热力学性质
defines the thermodynamic properties of the system.
这就是为什么围棋上这些形状相似的分布
That’s why thesesimilarly-shaped distributions
能够与同样的宏观态相对应
on the Go board correspondto the same macrostate,
而那些集中于一侧的分布情况却不行
while the clusteredspread does not.
所以当一个系统自动运行足够长时间
OK. So if you leave a system alone long enough,
系统中的粒子和能量会呈现所有可能的不同形态
its particles and its energy will find its way into all the different forms that are possible.
绝大多数可能的能量分布
The vast majority of possibledistributions of energy
使系统非常接近一个宏观状态
leave the system very closeto a single macrostate,
那就是热平衡状态
that’s the state of thermalequilibrium,
在这个状态下 能量最大程度地分散
in which energy is maximally spread out
并且温度 压力 密度 体积等参数值
and temperature, pressure, density, volume, etc.
和经典热力学预期的数值一致
have the values we expect from classical thermodynamics.
统计力学阐述了大规模系统特性的由来
Statistical mechanics tells uswhy large-scale systems have the properties they do,
但这与熵有什么关系呢?
but what does this have to do with entropy?
路德维希·玻尔兹曼也对此做出了解答
Well, Ludwig Boltzmann figured that out, too.
玻尔兹曼方程告诉我们
The Boltzmann equation tells us that
熵是两个部分的乘积 分别是
entropy is the logarithm of thenumber of microstates
微观态中与宏观态一致的个数对数
consistent with the current macrostate
和玻尔兹曼常数
times the Boltzmann constant.
所以我们均匀混杂分布的围棋棋盘具有高熵
So our smoothlyspread out equilibrium Go board has a high entropy
而棋子集中于一侧分布的棋盘具有低熵
and our clustered board has low entropy.
顺便说一句 有一些特殊的微观态
By the way, there arecertain special microstates,
其粒子的特殊排列看似高度有序
special arrangements of particles that look highly ordered
但仍然与它们的高熵宏观态一致
but are still consistent with theirhigh-entropy macrostate.
例如 当我们想在相空间中画画或写字时
For example, if we try todraw pictures or write words in phase space,
我们就会产生一种普遍的困惑
this is where get to a point of common confusion.
秩序和低熵状态下是不一样的
Order is not the samething as low entropy,
热力学第二定律也并不总表明一种混乱的趋势
and the second law isn’t alwaysthe tendency towards disorder.
在热力学的熵中
In thermodynamic entropy,
仅有一些能够改变热力学性质的
the only special arrangements of particles thatchange entropy
独特的粒子排列才能改变熵值
are the ones that change thethermodynamic properties,
排列组合成一些单词或是弄乱房间是没法奏效的
not the ones that spell out cuss words or mess up your room.
为了进行更深入的理解
To get deeper into that,
我们需要谈一谈信息熵
we’ll need to talk about information entropy,
在黑洞热力学中我们也会引入这一概念
which we’ll also need for blackhole thermodynamics
之后会再出一集对此进行详细讲解
and will take another episode.
好 所以用来解释热平衡的宏观态
OK. So the macrostate that definesthermodynamic equilibrium is,
从定义上说 将拥有最大量的微观状态
by definition, the one with the most microstates
也意味着其具有最大熵
which also means the maximum entropy.
任何处于不平衡状态的系统 其熵值都会上升
Any system not in equilibriummust increase in entropy,
这不过是因为 在未来的任何一个时间点
simply because at any future time,
它当时所呈现的宏观态将最有可能成为
it’s current microstate will most likely be
微观态的一种更加普遍的类型
one of the more common types of microstate.
这种情况假定无外力介入系统
This is assuming you don’t forcethe system from the outside.
我是指 也可以移动棋子
I mean, it’s possibleto take each Go stone
将其放置在特定的位置上
and place it on a particular spot
来构建一个独特的微观态
to construct a special microstate
或者使用真空管和玻璃墙
or to use a vacuumpump and a glass wall
将所有空气移动至房间的一侧
to move all of the air to one side of the room.
这两种情况中 可产生的微观态的数量在减少
In both cases, you are reducing the number of accessible microstates
从定义上来说 熵值也必定减少
which, by definition, must reduce entropy.
但是为了达到这一目的 必须引入一个外部的能量源
But to do so, you must introduce an external source of energy.
当热量在系统和外部环境间流动时
Heat must flow between yoursystem and the outside universe
它必然会使整个外部环境的熵值增加
in a way that increases the entropy of the universe as a whole.
无疑 统计力学指向熵和热力学第二定律
Statistical mechanicsinevitably leads to entropy and the second law,
这是由统计力学中毋庸置疑的根本规律所决定的
and it does so by something so fundamental and basicthat it’s impossible to deny.
它源起于对能量分布方式的计算
It comes from counting the waysthat energy can be distributed.
与这种计算相似
The inevitability of the rise of entropy
熵增的必然性也同样重要
is as fundamental as counting.
这也是为什么爱因斯坦和爱丁顿对此坚信不疑
That’s why Einstein and Eddingtonwere so sure of it.
但是熵也是具有统计学意义的
But entropy is alsostatistical
它产生于运动定律下的粒子行为
and emerges from behavior of particlesunder the laws of motion.
在这点上 热力学第二定律
This is where the second law
似乎提供了一些关于宇宙的新见解
appears to add something new to the universe
这些见解在宇宙基本定律中并未涉及到
not seen in the more fundamental laws.
这就好比插入时间之箭
It seems to add the arrow of time.
运动定律 不论是牛顿定律还是量子力学
See, the laws of motion,whether Newtonian or quantum mechanical,
都不关注时间走向
don’t care about the direction of time,
但热力学第二定律
and yet, the secondlaw of thermodynamics
清晰地展示了过去和未来
clearly distinguishes betweenthe past and the future.
在之前有关生命物理的一期视频中
We talked a little about this in our episode on
我们只粗浅地了解了
the physics of life, where we saw how entropy
熵是如何推动系统复杂程度消长的
drives both the increase and decay of complexity.
与“熵”类似 时间这一概念
It’s almost like the concept of time
就如同是自然形成的 并具有统计学意义
is emergent and statistical, just like entropy.
同样 我们还会在将来继续深入挖掘
Again, we’ll delve deeperinto this in the future,
但现在请注意控制你所能产生的微观态的数量
but for now, please be careful to keep your number of accessible microstates low,
避免热力学平衡
avoid thermal equilibrium,
保持良好的宏观状态
and keep being that brilliant macrostatethat is you,
直到下周在“PBS太空”栏目再会
until I see you next week on”Space Time.”
统计力学这一学科
The field of statistical mechanics
可让我们更深入地探索宏观领域及量子领域的运作方式
has given us some of the most profound insights into the working of both the large-scale and quantum realms.
令人惊讶的是 这一学科的基石是概率论
Stunningly, its foundations are in probability theory.
为了真正弄懂统计力学 你必须学习概率的相关知识
To really get stat mech,you have to get probability.
Brilliant.org上有关于概率的精品课程
Brilliant.org has a greatcourse on probability
该课程的稳固基础在于基于练习的学习模式
that’s solidly founded onexercise-based learning.
老实说 练习是攻克数学的唯一秘诀
Honestly, that’s the only way to get math, to do it.
快去看看吧 因为未来我们还会深入探讨统计力学以及熵
Check it out, because we’ll be doing more stat mech and delving deeper into entropy in the future.
学习物理不仅需要了解事实和记忆定律
Learning about physics is muchmore than facts and memorizing.
你只有找对方法 才能以全新的方式去探讨宇宙本身
When done right, it gives you a whole new way to look at the universe itself.
Brilliant网站 找对方法学习数学和科学
Brilliant, Math and Science Done Right,
很乐意赞助“PBS太空”栏目
is proud to support”Space Time.”
想了解更多内容 请前往brilliant.org/spacetime
To learn more about Brilliant,go to brilliant.org/spacetime.
[音乐播放]
[MUSIC PLAYING]

发表评论

译制信息
视频概述

追根溯源,一起探究“熵”的奥秘。

听录译者

收集自网络

翻译译者

努力努力再努力

审核员

审核员YZ

视频来源

https://www.youtube.com/watch?v=kfffy12uQ7g

相关推荐