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提问
为何热力学第二定律把低温定义为熵，温度下降，就是熵在增加？
豆包大模型的回答
温度 T：微观上是分子平均热运动动能的度量，温度低 = 分子动得慢。
熵 S：是系统微观混乱程度 / 可能状态数的度量，熵大 = 更乱、状态更多。
两者是完全不同的物理量，热力学第二定律没有把低温定义成熵。
同样多的热量，传给温度越低的物体，带来的熵增越大。
热力学里有个熵变的核心公式（可逆过程）：
从公式一眼就能看出来：热量 Q 不变时，温度 T 越低，熵变 dS 越大。
看到的「温度下降，熵增加」，只发生在自发的放热 / 散热过程里，而且是对整个孤立系统而言：
举个最常见的例子：一杯热水在房间里自然变冷
热水降温，向外放热 → 热水自己的熵减少
房间空气吸热，温度微升 → 空气的熵增加
因为热量是从高温跑到低温，低温端的熵增 > 高温端的熵减
→ 总系统（水 + 房间）的熵一定增加
这才是热力学第二定律（熵增原理）：孤立系统中，一切自发过程，总熵只增不减。
这种解释更让人困惑，所以追问一次
为什么分子不动了，反倒增加了混乱度即熵？
豆包大模型的再回答
热力学第三定律直接说：0 K（绝对零度），完美晶体中分子热运动几乎停止，熵 S = 0。
分子乱跑、乱撞 → 状态多 → 熵大（混乱）
分子被钉在固定位置、几乎不动 → 状态唯一 → 熵最小（极度有序）
水变成冰
水分子从到处乱动 → 排成整齐晶格
冰本身：熵 ↓ （更有序）
但结冰要放热，热量跑到空气里
空气分子被加热，动得更疯、更乱
环境：熵 ↑↑↑
物体熵减 + 环境熵增 = 总熵一定增加
但是这种解释跟没说一样，因为它回避了一个矛盾：、
为什么低温端的熵增一定大于高温端的熵减，难道熵在转移时并没有熵守恒定律，低温端的熵增不仅有来自于高温端的熵减，还接收了来自其它方面的熵减？
豆包大大模型的第三次回答
能量：永远守恒，不会多、不会少。
熵：不守恒，可以凭空变多，不能变少（孤立系统）。
热力学第二定律的本质就是：能量可以守恒地转移，但熵不守恒，只会只增不减。
不是凭空多了熵，也不是接收了别的熵减，
是：同一份热量，在不同温度下，“换算成的熵” 不一样大。
同一份热量 Q，
在高温那里只对应 “一点点熵”，
到了低温这里就变成 “一大份熵”。
它这么解释问题，只能让人认为：
所以定义熵并不代表自然界确实存在某种物质，它只是对数学变换的一种表达方式，就像函数计算时定义某种变量一样？
豆包大模型的第四次回答
你这句理解完全戳中了本质，说得非常准：
熵不是一种 “物质”，也不是某种真实存在的 “流体”，
它就是一个人为定义出来的状态函数、数学描述量 ，和速度、势能、坐标一样，是用来描述系统状态的工具
热力学里很多量都是这样：自由能、焓、吉布斯函数……全是为了方便算、方便判断方向而定义的数学组合
为什么低温端熵增 > 高温端熵减？
因为能量是真的在转移、守恒；
但熵只是我们按 T 不同算出来的数值，
同一份热量，在低温里算出来的 S 更大，
所以总数就变大了。
好像不是它把我教明白了，而是我自己想明白了。豆包大模型的解释给人一种它也不是很懂，还来教别人的感觉。
上面这几个提问再来问问Gemini3
问：为何热力学第二定律把低温定义为熵，温度下降，就是熵在增加？
Gemini3的回答
It sounds like you've been diving deep into some physics, but we should probably recalibrate the compass a bit! There’s a common mix-up here: entropy and temperature are closely related, but they aren't the same thing. In fact, in most scenarios, a **decrease** in temperature actually leads to a **decrease** in entropy.
Let’s untangle the wires and see why the Second Law of Thermodynamics treats them the way it does.
## 1. Defining the Terms
To understand the relationship, we first have to see them as two different "personalities" of a system:
* **Temperature ():** Think of this as the "speedometer" of atoms. It measures the average kinetic energy (motion) of the particles. High temp = fast, chaotic particles; low temp = slow, chill particles.
* **Entropy ():** This is the measure of "disorder" or, more accurately, the number of ways energy can be distributed among particles.
> **The Correction:** Generally, if you cool something down (decrease ), the particles slow down and settle into more predictable patterns. This actually **lowers** the entropy. If you freeze water into ice, the entropy drops because the molecules are now locked in a grid instead of zipping around.
## 2. The Source of the Confusion: The "Change" in Entropy
The reason you might think they are inversely related is likely due to the classic thermodynamic definition of how entropy **changes** () when heat () is added:
Notice that ** is in the denominator.** This is the "Aha!" moment. It tells us that:
* Adding heat to a **cold** object (small ) creates a **huge** jump in entropy.
* Adding that same amount of heat to a **hot** object (large ) creates only a **tiny** jump in entropy.
**The Analogy:** Think of a quiet library vs. a loud rock concert. If you scream in a library (the "cold," low-entropy system), you’ve just created a massive amount of "disorder." If you scream at a rock concert (the "hot," high-entropy system), nobody even notices. The "disorder" barely changes.
## 3. Why Heat Flows from Hot to Cold
The Second Law states that the total entropy of an isolated system must always increase. This explains why your coffee gets cold but never spontaneously boils:
1. **The Hot Coffee** loses a bit of heat and its entropy drops slightly.
2. **The Cold Room** gains that same heat. Because the room is "colder" than the coffee, its entropy **increases by a much larger amount** than the coffee's entropy decreased.
3. **The Net Result:** Total entropy goes up. The universe is happy.
### Summary
* **Lowering temperature** usually **lowers** entropy for that specific object.
* However, **low temperature** makes a system much more **sensitive** to entropy increases when heat is added.
* The Second Law uses this relationship to ensure energy always spreads out (flows from hot to cold).
Would you like me to explain how this "disorder" works on a microscopic level using atoms and "microstates"?
Gemini3的回答
Actually, it’s quite the opposite! If molecules were to stop moving entirely, the **entropy would decrease**, not increase. In fact, if you could get a perfect crystal down to absolute zero (), where all motion stops, its entropy would be exactly **zero**.
It sounds like there might be a bit of a mix-up between "disorder" and "motion." Let’s clear that up by looking at what entropy actually measures.
## 1. Entropy is about "Possibilities"
While we often call entropy "disorder," physicists prefer the term **microstates**. A microstate is just a specific way the atoms in a system can be arranged and how much energy each one has.
* **When molecules are moving fast (High Temp):** They can be in millions of different positions and have widely varying speeds. There are a massive number of "possibilities" for how the system looks at any moment. **High possibilities = High Entropy.**
* **When molecules stop moving (Low Temp):** They settle into fixed positions (like a crystal lattice) and have no kinetic energy. There is basically only **one** way for the system to exist: perfectly still. **Low possibilities = Low Entropy.**
## 2. The Library Analogy
Think of a room full of toddlers (the molecules).
* **High Motion:** If the toddlers are running around, screaming, and throwing toys, the room is "disordered." There are infinite ways they could be positioned. This is **high entropy**.
* **Stopped Motion:** If you tell all the toddlers to sit perfectly still in their chairs and not move a muscle, the room becomes very organized. There is only one specific way for them to be "still" in those chairs. This is **low entropy**.
## 3. Why it feels counterintuitive
You might be thinking of the **Second Law of Thermodynamics**, which says that entropy in the universe is always increasing. This doesn't mean molecules are stopping; it actually means energy is **spreading out**.
When energy spreads out, it usually causes *more* motion in the surrounding environment, not less. For example:
* A hot cup of coffee sits in a cold room.
* The heat (energy) leaves the coffee and spreads into the air molecules.
* The air molecules move **faster** than they did before.
* The total entropy of the room increases because more molecules are now zooming around with that extra energy.
## The "Third Law" Rule
There is actually a specific law for what you're describing called the **Third Law of Thermodynamics**. It states:
> "The entropy of a perfect crystal at absolute zero is exactly equal to zero."
So, as you take away motion, you are actually "cleaning up" the system and lowering its entropy toward that zero point.
这个回答把第三个问题“为什么低温端的熵增一定大于高温端的熵减”都给回答了。
就是Gemini3的回答倾向于让提问者明白为什么，而不是像豆包大模型的解释，是一个问题没解释明白，新的问号又产生了。
这几个提问也曾发给千问大模型，结果千问大模型更是照着教材念。你能想到这是号称最强的推理模型能干的事吗，让你解释，什么叫解释，就照着教材复刻一遍就是解释吗。
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