It helps explain why physical processes go one way and not the other:

有助於解釋是此非彼的物理現象

why ice melts,

冰為什麼會融化？

why cream spreads in coffee,

奶油為什麼會在咖啡裡散開來？

why air leaks out of a punctured tire.

為什麼穿了孔的輪胎會漏氣？

It's entropy, and it's notoriously difficult to wrap our heads around.

這是「熵」的概念，非常難以理解

Entropy is often described as a measurement of disorder.

有個說法常把熵 用來衡量不規則的程度

That's a convenient image, but it's unfortunately misleading.

雖然合宜，卻很容易誤導

For example, which is more disordered -

例如，下列哪種情形比較不規則呢？

a cup of crushed ice or a glass of room temperature water?

一杯碎冰，還是一杯室溫的水？

Most people would say the ice,

大多數人認為冰比較不規則

but that actually has lower entropy.

但實際上冰的熵值比水低

So here's another way of thinking about it through probability.

另一種理解熵的方法是透過機率

This may be trickier to understand, but take the time to internalize it

雖或不易理解，但請耐心內化

and you'll have a much better understanding of entropy.

就會更理解熵

Consider two small solids

想像兩小塊固體

which are comprised of six atomic bonds each.

各自有六根原子鍵

In this model, the energy in each solid is stored in the bonds.

這模型裡的能量存在固體的原子鍵裡

Those can be thought of as simple containers,

可以把原子鍵想成簡單的能量容器

which can hold indivisible units of energy known as quanta.

裡面裝著不可分割的 能量單位「量子」

The more energy a solid has, the hotter it is.

固體的能量越高就越熱

It turns out that there are numerous ways that the energy can be distributed

這兩個固體

in the two solids

有許許多多的能量分佈方式

and still have the same total energy in each.

而各自的總能量不變

Each of these options is called a microstate.

每一種能量分佈方式稱為一「微態」

For six quanta of energy in Solid A and two in Solid B,

假如固體甲有六個量子，而乙有兩個

there are 9,702 microstates.

那麼就共有 9,702 種微態

Of course, there are other ways our eight quanta of energy can be arranged.

當然還有其它分派八個量子的方式

For example, all of the energy could be in Solid A and none in B,

例如，固體甲擁有八個量子 而固體乙一個也沒有

or half in A and half in B.

或者甲乙各分一半

If we assume that each microstate is equally likely,

如果假設每種微態發生的機率相等

we can see that some of the energy configurations

就會看到某些能量分佈狀態

have a higher probability of occurring than others.

發生的機率高過其他狀態

That's due to their greater number of microstates.

原因是它們的微態總數比較多

Entropy is a direct measure of each energy configuration's probability.

熵直接衡量每種能量分佈狀態的機率

What we see is that the energy configuration

呈現出的是

in which the energy is most spread out between the solids

這兩個固體的能量最分散的時候

has the highest entropy.

熵值最高

So in a general sense,

一般而言

entropy can be thought of as a measurement of this energy spread.

可把熵想成是能量散佈的指標

Low entropy means the energy is concentrated.

低熵值代表能量集中

High entropy means it's spread out.

而高熵值代表能量分散

To see why entropy is useful for explaining spontaneous processes,

為要理解怎樣用熵解釋自發過程

like hot objects cooling down,

像是熱的物體冷卻下來

we need to look at a dynamic system where the energy moves.

必須看能量的動態流動

In reality, energy doesn't stay put.

實際上，能量並非靜止不動

It continuously moves between neighboring bonds.

而是持續在相鄰的原子鍵中移動

As the energy moves,

隨著能量移動

the energy configuration can change.

能量的分佈跟著改變

Because of the distribution of microstates,

根據微態的分佈

there's a 21% chance that the system will later be in the configuration

有 21％ 的機率

in which the energy is maximally spread out,

後來會進入能量最分散的狀態

there's a 13% chance that it will return to its starting point,

有 13％ 的機率回到初始狀態

and an 8% chance that A will actually gain energy.

還有 8% 的機率 固體甲會增加能量

Again, we see that because there are more ways to have dispersed energy

再次重申，因為分散能量

and high entropy than concentrated energy,

高熵值的微態總數 比能量集中的還多

the energy tends to spread out.

因而能量趨向分散

That's why if you put a hot object next to a cold one,

這就是為什麼把熱的物體 和冷的物體擺一起

the cold one will warm up and the hot one will cool down.

冷的會變熱，而熱的會變冷

But even in that example,

但是同一個例子

there is an 8% chance that the hot object would get hotter.

也有 8％ 的機率 熱的物體會變得更熱

Why doesn't this ever happen in real life?

為什麼現實生活裡沒發生這種情形？

It's all about the size of the system.

原因在於系統的規模

Our hypothetical solids only had six bonds each.

我們的模型假設 只有六根原子鍵的固體

Let's scale the solids up to 6,000 bonds and 8,000 units of energy,

如果增加到 6,000 根原子鍵 和 8,000 個單位能量

and again start the system with three-quarters of the energy in A

初始狀態仍是甲有四分之三的能量

and one-quarter in B.

而乙有四分之一的能量

Now we find that chance of A spontaneously acquiring more energy

就會發現甲自發獲得更多能量的機率

is this tiny number.

是個這麽微小的數字

Familiar, everyday objects have many, many times more particles than this.

日常熟知物體的粒子數遠比這多得多

The chance of a hot object in the real world getting hotter

所以現實世界裡 熱的物體變得更熱的機率

is so absurdly small,

小得荒謬

it just never happens.

乃至根本不會發生

Ice melts,

冰塊融化

cream mixes in,

奶油和咖啡混合在一起

and tires deflate

輪胎放氣

because these states have more dispersed energy than the originals.

都是因為這些狀態的能量 比原先狀態的更分散

There's no mysterious force nudging the system towards higher entropy.

並不是某種神秘的力量 驅使系統傾向微調至更高的熵值

It's just that higher entropy is always statistically more likely.

而是因為統計上高熵值更可能發生

That's why entropy has been called time's arrow.

這就是為什麼熵又被稱為時間之箭

If energy has the opportunity to spread out, it will.

如果有機會分散能量，就會分散能量