1840Indian rebirth

Ma Shao just talked about Clausius entropy, but the connotation of entropy is much more than that.

In later generations, the concept of entropy was regarded as the most popular among the most popular, and all disciplines discussed it endlessly.

Entropy has been discussed for a long time in natural science and philosophy. It has also been a guest in literature, film and television works, and there are countless concepts and theories extended by it.

Not to mention discussions in other disciplines, within the scope of physics, entropy also has three important historical stages - Clausius entropy, Boltzmann entropy, and information entropy.

Each stage of change means that humans have a deeper understanding of the essential laws of the world.

What he will talk about next is Boltzmann entropy, which is also the most commonly discussed entropy in later generations.

As for information entropy, he didn't plan to talk about it. After all, it was something a hundred years from now, and it was a bit too advanced.

"For a certain substance, the entropy of gas is greater than that of liquid, and the entropy of liquid is greater than that of solid. Can we imagine that entropy is actually a measure of chaos and disorder?" Ma Shao said slowly.

"After all, it is obvious that when a mass of matter changes from solid to liquid or gas, its structure becomes more chaotic and the particles inside move more wantonly."

Ma Shao walked to the blackboard and continued: "Intuition or paranoia tells me that this idea is correct... So, is there any way to give this idea a mathematical expression?"

Hearing this, many people felt their imaginations were opened and they were amazed.

"How chaotic is matter? How can this be expressed mathematically?" People can't help but wonder.

"Can this really be done..."

Ma Shao picked up the chalk, wrote Boltzmann's formula directly on the blackboard, and said: "Of course there is a way, this is the true face of the second law of thermodynamics."

Although Boltzmann's formula is simple, if you want people to understand it, some explanation is indispensable.

Looking at the confused physicists, Ma Shao did not rush to explain the formula itself, but said: "Let us imagine a scene like this. In a box, there are two hydrogen molecules..."

"Molecule?" Before he finished speaking, there was a burst of discussion in the audience.

At this time, people's understanding of elementary particles is extremely lacking and inconsistent.

Atomic theory is still controversial, and few people agree with molecular theory.

"Or it's okay to say atoms." Ma Shao thought for a moment and changed his words.

"I don't agree with atoms. They can't be seen or touched. It's all conjecture. Matter should be infinitely divisible!" A physicist immediately protested, with a somewhat fierce attitude.

Mashao smiled: "Conjecture? In my opinion, infinite divisibility is a conjecture without any factual basis. When have humans ever made infinite divisions?"

"From ancient times to the present, we have been performing limited divisions. Based on the principles of experience, the most reasonable conjecture is that matter has limited divisibility."

"Atoms are indeed beyond our senses, but infinite divisibility is not only beyond the senses, but even beyond all experience, and is even more illusory."

"It's like an ant walking on the table. Every step it takes is the same as the previous step. So it naively thinks that the wooden surface under its feet extends infinitely. How ridiculous this is."

Atomic theory was one of the most controversial topics in academia at this time, and various factions had been arguing for a long time.

In fact, this debate would continue until Einstein's time.

The tone of Ma Shao's words was not peaceful, which aroused people's heated discussion even more.

"He is right, atomism is the truth!"

"Nonsense, Dalton's theory is simply heresy!"

“The followers of Berzelius are all @%/!”

"You keep scolding me!"

For a moment, the scene seemed a little out of control.

Seeing this, Ma Shao quickly changed the topic: "Regarding atomic theory and molecular theory, I think Brownian motion is a case worthy of attention. I will publish a paper to elaborate on my views soon. I welcome your criticism... As for now

, this is not the topic of my speech.”

Fortunately, the professors were of good quality and did not really make the situation get out of control, and it calmed down after a while.

Ma Shao drew a schematic diagram on the blackboard and continued: "Whether it is an atom or a molecule, or any other tiny particle, it does not affect my subsequent discussion. Suppose there are two hydrogen atoms in a box - let's just say this

explain."

"There is no doubt that macroscopically, there are three distributions of these two hydrogen atoms, all on the left, one on the left and one on the right, and all on the right."

"On the microscopic level, the corresponding state numbers of the three are one, two, and one... Let us draw a curve to represent it."

"Assuming that each microstate has an equal probability of occurrence, this curve actually reflects the distribution probability of atoms."

"Obviously, as the number of atoms increases, this curve will become narrower and narrower, and atoms will have a greater probability of being evenly distributed in space. This is consistent with our life experience - air can diffuse spontaneously without

It will shrink spontaneously, and it is almost impossible for us to encounter a situation where air atoms are concentrated in one place and cause people to suffocate to death."

After the narration, Ma Shao brought people's attention back to Boltzmann's formula: "Now we can understand the meaning of this formula. When the entropy of a system is maximum, it is in the most chaos and corresponds to the largest number of microstates.

Macrostate.”

The scene was quiet for a while.

Most people only vaguely understand it, and do not immediately understand the mystery of Boltzmann entropy.

This is reasonable, after all, Mashao has just given the Clausius entropy, and many people have not even understood the Clausius entropy yet.

But this is not a problem for Ma Shao. As a teacher, he has seen this state among all his students.

His solution is very simple, which is to constantly give examples, make analogies, and ask questions, just like engineers training artificial intelligence, instilling a large amount of data into students' minds and labeling it.

This may be the only way. After all, many cognitions are indescribable and can only be obtained through training. For most people, intensive trial and error and iteration are a stage that must be experienced in professional learning.

Then Ma Shao began to explain like a storm, bringing up many cases from daily life and setting up questions to examine, exactly like a teacher giving a lecture.

He is fully qualified to do this. As an outstanding teacher one hundred and eighty years later, if he cannot teach these nineteenth-century predecessors, it probably only means that human beings are a race that has not made progress.

As the lecture progressed, even the professors themselves had to admit that the Indian chief with the yellow face in front of them was an impeccable instructor.

In the academic halls of today's world, every tone of his voice seems to be an echo of the ancient Greek sages.

In the end, except for a few ignorant professors and seriously biased physicists like Faraday, most of the audience here understood the concept of Boltzmann entropy.

However, understanding does not mean agreement.

"Do you still have any questions?" Ma Shao said, and slightly restrained his teacher's posture to make himself look more humble, "If you have any questions... well, my friends can raise their hands."

As soon as he finished speaking, a man in his early thirties raised his hand. His position was relatively far back, which forced him to stand up. He was obviously not a highly qualified scholar.

"What do you call it?" Ma Shao said casually.

"George Boole," the man said.

Hearing this name, Ma Shao couldn't help but be startled.