Xu Shengzhou looked around and asked with some uncertainty: "Is it right here?"

"No?" Xue He asked.

Xu Shengzhou took out his notebook from his backpack: "Maybe I will have more questions, and many things need to be deduced. Without a whiteboard, I'm afraid it won't be clear just by talking."

The female graduate student with a burning spirit of gossip had been watching the crowd. After hearing this, she immediately said: "We have prepared a lot of conference rooms for this meeting. They are nearby. There are whiteboards and markers in them. If you want to discuss it, you can

Go there."

The atmosphere is so great here that it would be a bit rude not to go.

Xue He led everyone to find a conference room. As soon as he sat down, he put on a posture of letting the wind blow from east to west but not moving: "Any questions? Just ask!"

Xu Shengzhou did not greet him politely. He directly picked up the marker and wrote while saying: "The fluctuation dissipation theorem connects the fluctuation correlation of the statistical mechanics system with its response to external stimuli with a clean equation. But it

It is derived from the infinitely slow adiabatic process. Generally, the process is completed in a finite time. For the non-adiabatic process with a finite time, how to understand the fluctuation dissipation theorem?"

An expert will know if there is one as soon as he reaches out his hand.

After hearing Xu Shengzhou's question, Xue He couldn't help but straighten up slightly. Although this kid had been bragging a bit before, this question was asked above the standard, indicating that he had at least studied the textbook carefully and his basic skills were still very solid. In other words

In other words, you can still save it: "This question is interesting. What do you think?"

Xu Shengzhou said: "My idea is to focus on the impact of non-adiabatic processes on the fluctuation dissipation theorem, but then——"

Xue He thought for a moment: "Try using perturbation theory? This should be able to deduce the non-adiabatic modification of the fluctuation dissipation theorem, and discuss the resulting quantum phase transition. - This is a good question, if you write it carefully

, can produce a good paper!"

Xu Shengzhou didn't care about this, at least he didn't care much about such insignificant papers. In his opinion, the opportunity to consult professionals like Xue He was even more rare: "The second question is about stochastic dynamics.

.My idea is, can we establish a stochastic dissipation relationship based on the fluctuation dissipation theorem?"

Xue He straightened up after hearing this: "Random dissipation relationship? Let's talk about it in detail!"

Xu Shengzhou said: “Through the singular decomposition of the dynamic norms, a method of explicit construction of potential energy is given... It is not difficult to prove that in any stochastic dynamic process, a potential energy function can always be constructed to describe it... It can even be

Extend this relationship to nonlinear partial differential equations with infinite degrees of freedom, connect random fluctuations with the global situation, and construct a global situation/Lyapunov functional of the system under the framework of the one-dimensional noise-stable SKS model. If

My inference is correct, this potential energy construction method should be universal."

Only the graduate students watching in the audience were confused.

Xue He was calculating nervously, trying to keep up with Xu Shengzhou's ideas.

Hu Yuanke had already started to slap his thigh: "Wonderful! What a genius idea! I think it can open up a new solution for similar nonlinear systems, such as the Navier-Stokes equation. How did you get such a big brain?

?How did you come up with this?"

Xu Shengzhou scratched his head: "According to mathematical ideas, it is not difficult to deduce it. The key is, does it make sense in physics? In other words, does it make sense in physics?"

The reason why he said this was because he learned from past mistakes.

Clausius, the famous physicist and one of the main founders of thermodynamics, came up with a very large number when calculating the average speed of molecules. He proudly showed the result to his wife, who was very surprised.

Puzzled: "But when I was chopping onions, I didn't shed tears so quickly!"

Then there is the concept of mean free path.

Hu Yuanke said: "Why is it meaningless? It is very meaningful! And it is of extraordinary significance! Go back and write it down quickly, and then send it to me to help you check. My email address is on the personal homepage of the school website. You don't need me to teach you how to find it.

Right?"

"No, no need. Then I thank you first!"

Hu Yuanke laughed: "Thank you for what? If you really want to thank me, come to our physics department to study for a Ph.D. tomorrow. The Nobel Prize in Physics is not as prestigious as the Fields Medal, and it has more money. The key is that the Fields Medal comes only once every four years.

The winner must be under 40 years old. Unlike the Nobel Prize, which is awarded every year, you will have a chance until you are 90 years old!"

——In 2019, American physicist John Goodenough (surname also Goodenough, "good enough") won the Nobel Prize in Chemistry at the age of 97, making him the oldest winner of the Nobel Prize.

Records. Of course, it is a routine operation for a physicist to obtain a chemist.

Before Xu Shengzhou could think of how to answer, Mr. Hu suddenly waved his hands in frustration: "Forget it! Lao Cheng is an academician, I can't compete with him."

It was obviously a complaint, but Xu Shengzhou clearly heard the desolation and loneliness in it.

At this time, Xue He finally understood Xu Shengzhou's idea, and praised him repeatedly with paws: "Xiao Xu is indeed a mathematical wizard! He uses mathematical methods to solve physical problems, and his fantastic ideas are refreshing. If you register early, submit this

A paper, I want you to give a report at the meeting no matter what!"

Xu Shengzhou waved his hand and said: "I just thought of it a few days ago. How could I dare to write it casually without your approval?"

In his opinion, it is best to publish papers. After all, no one would dislike having many papers to his name. But his purpose of studying statistical physics is not to publish physics papers, nor to become a physicist, but to become a physicist.

If we use the theories, methods and logic to solve the Hodge conjecture, we will naturally not think about writing these things out and publishing them.

This chapter is not over yet, please click on the next page to continue reading!

Xue He sighed: "Sure enough, stones from other mountains can attack jade!"

Xu Shengzhou continued to ask: "My third question is about Maxwell's demon. As a core concept of modern thermodynamics, entropy production quantifies the energy dissipation in a random system... One of the basic properties of entropy production is that it follows the Jarzynski identity

and the integral fluctuation theorem, which can be regarded as the generalized second law from a microscopic perspective... In order to analyze the influence of Maxwell's demon, I tried to construct an entropy production that does not comply with the Jarzynski equation. According to the Sagawa-Ueda theorem, Maxwell's demon extracted

The work cannot exceed the information obtained on its average... I construct different non-normal entropy productions by ignoring some part of the contribution of Maxwell's demon. Accordingly, there are different fluctuation theorems for these entropy productions, which will lead to different work or heat.

Second Law Inequality. So the question is, which inequality should I use more appropriately?"

It seems that Maxwell’s Demon is a real demon.

Not only were the graduate students confused, but Xue He was also confused. Even Mr. Hu repeatedly interrupted Xu Shengzhou's narration: "Please stop for a moment, why can you deduce this step?"

"Obvious!"

Mr. Hu was so angry that the corners of his mouth twitched: "Why is it so obvious? Could it be that he was like Fermat, who was convinced that he had discovered a wonderful proof?"

"But in mathematics, it's really obvious!"

After Xu Shengzhou gave them some extra math and proved that "obviously" is really obvious, he was stopped again by Mr. Hu before he could speak for a few minutes: "How did you get this step?"

"By combining this formula, this formula, this theorem, and this inequality, we can get it by performing simple calculations."

Mr. Hu expressed that he wanted to curse: "It seems that you have redefined what 'simple' is!"

Xu Shengzhou had to spend more than ten minutes to calculate it for them personally. After he finished explaining, Hu Yuanke said: "Well, I didn't quite understand."

Xue He clasped his hands and said, "Me too!"

Xu Shengzhou was too lazy to go back and explain to them, so he simply asked the second question: "When the inequality of the second law is equal, it means that the system is in a thermal equilibrium state. However, when the system is controlled by Maxwell's demon, it should be in a non-equilibrium state. This

shows that if Maxwell's demon is working effectively, then the equations in the second law in the previous framework do not always hold. I checked some information that shows that there is additional energy dissipation when the system is in a controlled non-equilibrium state

.So, where does this energy dissipation come from?”

Hu Yuanke said: "Why don't you explain it to us in detail?"

Xue He clasped his hands and said, "Me too!"

Xu Shengzhou felt very tired: "Maybe this problem is more complicated. How about I ask the next question, which is about nonlinear reversible conservative time-delay systems."

Xue He's face was full of "What are you talking about?" expression.

Xu Shengzhou quickly changed: "Then I would like to ask you about the theory of non-unitary transformations and the problem of resonance singularities in non-integrable systems, can you?"

Xue He was completely numb.

Looking at Xue He who had seriously doubted his life and frequently looked at his watch to remind himself that enough was enough, Xu Shengzhou gritted his teeth: "The last question I want to ask is, can we understand dissipation without causality?

”

"What do you mean?"

Xu Shengzhou said: "As we all know, the theory of relativity makes some counter-intuitive facts possible, such as a state that is stable in one reference system but unstable in another reference system. So how do we test whether Lorentz is satisfied?

Stability of the state of magnetic invariance? Should the relationship between perturbation and light cone be mainly considered?"

Xue He suddenly became energetic: "I read papers with similar issues when reviewing papers a few days ago, so I have a little understanding. Their general conclusion is that only when the disturbance can leave the light cone, two observers can judge whether a state is

Stability creates divergence. If a perturbation exits the light cone and its intensity changes with time due to dissipation, then there are always two observers who will have different opinions about the stability of the state. Therefore, stability is the Lorent theory of dissipation theory

This is an invariant characteristic if and only if it follows the principle of causality."

Xu Shengzhou was happy while remembering: Finally, my trip was not in vain.
Chapter completed!