Statistical Mechanics Lecture 1
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- Опубліковано 29 сер 2024
- (April 1, 2013) Leonard Susskind introduces statistical mechanics as one of the most universal disciplines in modern physics. He begins with a brief review of probability theory, and then presents the concepts of entropy and conservation of information.
Originally presented in the Stanford Continuing Studies Program.
Stanford University:
www.stanford.edu/
Continuing Studies Program:
csp.stanford.edu/
Stanford University Channel on UA-cam:
/ stanford
"My life has consisted in learning and forgetting and learning and forgetting and learning and forgetting statistical mechanics". It incredibly lightens me to hear this from one of the greatest minds we had in history!
Jajaja I definitely agree
Where does he say this?
@@BritishProudnShit 9:55
*we have
Lies again? Soccer mom
0:00:00 to 0:10:10 - Introduction to course
0:10:11 to 0:19:48 - Mathematics of probabilities
0:19:49 to 0:36:22 - Techniques for determining probabilities (Symmetries, experimental data or the systems laws of motion)
0:36:22 to 0:40:18 - Questions
0:40:19 to 0:54:25 - Liouville's theorem (Conversation of information)
0:54:26 to 0:58:18 - Simple definition of entropy
0:58:19 to 1:07:17 - Generalizing to continuous mechanics
1:07:18 to 1:12:55 - First law of thermodynamics
1:12:56 to 1:38:09 - Expanding the definition of entropy + examples
1:38:10 to 1:47:38 - Questions
THANKS!
You’re a very nice guy, thanks!!
A million likes for it!
I miss you at the other lectures (other than 2)
You are the man!
I love the way Susskind talks about physics and even just talks in general. His background as a plumber I feel is a boon to the communication of physics; talking to people like they are a normal joe and a potential scientist. Everyone can have access to these ideas. And they can be simple and elegant.
this guy is just incredible
he's moving from calculus, probability, topology, classical mechanics, thermodynamics etc at will
using just words
And an expert on quantum statistical mechanics, John von Neuman was an expert on that too, so von Neumann was most probably one of Leonard Susskind's heroes.
All of the cycles he is describing to illustrate probabilities are aspects of the study of permutations in modern algebra (which itself is tied closely to group theory).
I love the fact that, unlike most profs, he doesn't rush and he takes time to explain ideas.
Not quite my tempo! Are you rushing or are you dragging?
Professor Leonard Susskind not just teaches these complex topics in a simple way, but he also motivates you.
嗯，老头讲的不错
few are able to explain with such a degree of clarity, thank you mr. Susskind
I think no one can teach Physics better than Sir Leonard Susskind. He is amazing. He is a gift from Almighty God to us. I am a big fan. and one day i would want to take physical classes with Leonard. i think its my dream and it will come true very soon.
try v balakrishnan
Why is Mike Ehrmantraut teaching statistical mechanics?
Because no more half measures.
+Nikifuj908 combined with John Malkovich
Guss told him to do it.
Wanted to rival Walt's prowess as a chemistry teacher.
All of the above. And more . . . .
personally i think that people don t understand the quality of what they are consuming here. like" FOR FREE"
you should praise those teachers
I love how he takes his time explaining the main ideas. I wish my physics professors did that but because of either a lack of time, teaching ability or both, the material is rushed to the point I can barely understand anything in class. We would be better served with longer lectures like this I think.
I got a lecturer who just read from power point slides, I came to her class with zero and came out with zero. So sad 😢
I'm starting to think that online learning is much better... They don't bother to be precise nor specific enough for us to truly understand. I'm better off with my own research and resources, which much too often makes me ask the question: "What exactly am I paying for?". Basically, we study, research, and work out solutions on our own but pay for being bullied.
@@niamcd6604 agreed 👍
@@niamcd6604 The issue for me isn't that their not precise enough. It's that they try to fit too much into a lecture an hour or so long. If I try to understand an example that they work through in full mathematical detail by the time I have understood everything, they have covered the next 1 or 2 slides or are half way through the next example problem. Videos are much better for me because I can pause and rewind whenever I need to.
Zoom classes are the worst of both worlds because you get none of the benefits of videos and it is subpar compared to attending in person.
That's why if I ever become a teacher I'm going to create a You tube channel, so students can watch my lectures at their own leisure before or after class.
Thank you Dr. Susskind and Stanford for generously sharing this with the world.
I always love to watch Sir Ben Kingsley.
Leonard Susskind, my favourite black physics student
?
@@iconsumedmt1350 His t-shirt
That casual definition of a conservation law as the possibility space dividing up into cycles went by so quickly it didn't blow my mind until I rewatched.
Where??
1:30:20 "Two is the smallest number which is not one" I really like this statement.
the wealth of free information in the internet is astounding
Just bought the classic text, The Principles of Statistical Mechanics by Tolman with so much excitement. And, it’s a hardback version from the 40’s! S. Chandrasekhar once recommended the text to his brother to study for physics. You can just sense that this is a master text. A subject that gives you the power to analyze mechanical systems when their initial states are known only partially ? Count me in.
Thanks for the book recommendation and story behind it :D
So... did you read it?
Did anyone else laugh as hard as I did near the at the camera suddenly stopping and then zooming back in when Prof. Susskind asked if anyone had questions? It just looked to me like the lecture was all finished and the camera started zooming out like the video was about to end and the abrupt way he broke the silence followed by the camera stopping made it seem kinda like the camera person was surprised and thought "woops! He's still going. Better zoom back in."
I am yet too see the whole lecture
I have seen the complete set of videos Statistical Mechanics by Susskind. I can highly recomend the book "Fundamentals of Statistical and Thermal Physics" by F.Reif. It is Briljiant together with Lennys vidoes.
Best line 😂:
2 is the smallest integer which is not equal to 1 .
What?
Can anybody explain whats the case with (-infinity)
@@balasujithpotineni8184 OK, smallest positive integer. Don't bother too much about that line.
@@balasujithpotineni8184 yes, -inf is less than 1. But when I hear "smaller", I think of the magnitude (absolute value). So 1 is both smaller and more than -inf, -inf is both larger and less than 1
@@kennyimammahardika3868 -inf isn't an integer.
I love this guy
these lectures should be saved in a museum and protected for posterity. they are like a treasure of mankind
This is why the tution fees is extremely huge in comparison to my college I went. Nice lectures, challenging and optimistic preparing your brain to utilise the potential.
Watching these videos from Stanford and other prestigious universities; they don't seem much different than where I went to college and grad school. Just a plain old state school in Texas.
In many cases what separates the average student an elite university from the average student at a good state university is not necessarily that the former has vastly superior intellectual capabilities (although that is often true of their *best* students), but that elite university students have demonstrated great ambition and an incredible work ethic. The content of the classroom lectures is likely very similar, though the volume and difficulty of the problem sets and course projects is probably substantially different.
My own experience in taking and teaching courses as an undergraduate student at a good private university and a graduate student at a borderline-elite technical university was that the student bodies weren't that different entering as freshman, but that by graduation the latter were better at their craft due to the sheer volume of work completed during 4 years of frequent sleepless nights and the constant struggle to meet impossible deadlines and expectations.
It's certainly not for everyone, nor should it be. Many people aspire to obtain a stable, moderately high-paying job in an enjoyable profession, and to that end many universities will do a great job. The advantage of elite universities is building a network of people who will rise to high positions in society, as well as being surrounded by a culture which not only aspires to excellence, but demands it on a daily basis.
I think the main difference is more difficult exams.
@Nuclear Nadal I can go along with some of what you said except the part about sheer volume of work, impossible deadlines and sleepless nights. Give me a break. All college students go through that, not just the ones at elite universities. I sure did. I often wonder how my collegiate effort would have been received at an Ivy League institution, I always did whatever it took to make the grade. The coursework is harder you say? Well, I wouldn’t know but I’m sure even students at elite universities open their intermediate macroeconomics with calculus applications text books and have a good cry. My major was no picnic and I had some very bright classmates who were also pushed to their limits. A lot of us including me turned down admissions from more competitive institutions because our money went further elsewhere, not because we couldn’t gain admission. I turned down Rice and a classmate of mine declined the U. of Chicago. It’s just tough for me to imagine I would have put any more effort into my studies than I did. I’ll never know. Things are great for me. Over 30 years I’ve built a strong professional and social power base. Almost all of my friends are the same. Anyway, I’ve never regretted the decision I made.
speed set to 1.25, then it's perfect.
lol HI FIVE !!!!
THANKS.. IT LOOKS LIKE HE TOOK COFFEE TOO MUCH
more like 2.75x
pff.. those are rookie numbers. 2x is perfect.
You saved me sooo much time sir.
Thank you, Sir. You have changed the way of observing the physics. It's an amazing lecture!!!
The concept is so clearly presented....
I love this lecture
If he is right and statistical mechanics is the deepest aspect of physical reality, then I'd vote for Stirling's/de Moivre's approximation over Pythagoras' theorem or Euler's formula as the most important _practical_ result in all mathematics. Thanks Lenny.
Ever since Gus Fring died, Mike Ehrmantraut has had to take up a side gig teaching statistical mechanics to make ends meet.
My first time watching a Susskind lecture, though I know he's a famous dude. Love the dad vibes, haha.
Thank god I found this series. My final is next week. I did not expect people to upload videos of upper division physics courses.
Did you pass?
I have a PhD in chemical engineering, and got a's in all of my courses, EXCEPT! graduate course in Statistical Mechanics. God, that was hard.
So you graduated with a 4.0 in the graduate course? I suspect that you are lying. Nobody brags about having a phD, especially in the sciences and engineering. We like to be behind the scenes. Also how are you allowed to take a graduate course in statistical mechanics with no pre requisites?
John von Neumann made a notable contribution to quantum statistical mechanics, which Leonard Susskind has been involved with, so maybe von Neumann is one of Leonard's heroes?
Stat Mech was one of my favorite courses in grad school. I remember being so impressed that you could make some statistical assumptions and end up with the ideal gas law.
About the evolution of the states of the colours, where they evolve each microsecond, surely how often the observations take place will determine the outcome, if you measure each 6th microsecond you will get one answer all the time and conclude 100% probability of some colour, in fact, depending on frequency and the phase of your observations the outcome will vary, you would either need a very fast rate of observation or a completely random sequence of observations as to not bias the results
"You can predict the probability... but not when its going to happen" - the story of the market in a nutshell :)
at 1:13:20 professor Susskind says that temperature is a highly derived quantity "despite the fact that you feel it with your body", so he points out the contradiction of how temperature feels intuitive despite being a more mathematically-derived concept with respect to more primitive concepts like energy.
the thing is, in fact, you don't feel temperature at all, you feel THE FLOW OF THERMAL ENERGY. if i'm not mistaken minutephysics has done a video about it too.
Mathematicians invented and often manipulate the dirac delta function and it does appear in physics quite a bit e.g. the probability density function of photons of different frequency having their energy absorbed by a bound electron.
I wish I could ever get a chance to take a part in this kind of lecture in Stanford
My former math teacher would throw himself off a bridge if he saw What I am watching at 8 in the morning
If i was at his age, i would be sitting somewhere near the beach and enjoy the sunshine breeze, but he chooses to teach, SO MUCH RESPECT!
statistical mechanism is what only if you left it and discover how deeply it has effected on other subjects that you will discover how beautiful it is
Love the shirt, Susskind is most definitely invited to the cook-out !
his examples and analogies, uffff! , how does he come up with such great ideas...
Nobody does it better than Leonard "Leonardo" Susskind.
I just studied the quantum mechanics course and this looks even better :). I love the probability part, particularly the classes in the Markov chain as a conservation law. Is the relation between time spent at each state and probability a sort of baby ergodic theorem?
"I always start with coins, even when I teach Higgs Boson" Lol
About the -1 law of physics: what about quantum measurement? The information is lost there due to wave function collapse.
but the wave colapses as a pulse "particle" right?
I had 3 semesters of Engineering Calculus and this brings back memories........ Bad Memories......
Que lindo es tener este tipo de material a disposición de cualquiera que le interese y gratis!!
I always wonder what the camera operator thinks/how well they follow along during these recorded lectures.
Powerful speech professor, don't worry what happened at Berkeley last night brought Mr. Stephen Bannon 's name to public eyes!!
Beautifully explained!
57:45 a cool definition of entropy
This is the most beautiful piece of music I found in UA-cam
For those who have watched this series, can anyone give me a bit more information? Is this graduate level, and are all seven of these lectures a complete course?
I am not even a physics student but I study physics for recreation!!!
Ibn Sina r/iamverysmart
@@naderelsarrag r/iamveryunoriginal
@ibn sina.... what!!!!!! seriously,,,,,, we become fucked up by this. I'm a physics student
@@naderelsarrag huh?
I'm not in college or anything, I just like to get drunk and watch these videos 👍
This professor is just the best!
Amazing lecture, this will be my subway playlist!
For example, if you select a random number between 0 and 1, the total number of cases is infinity. Therefore, the probability to get exactly i = 0.5 (for example) is 1/infinity = 0.
You are correct about the PDF. I had a long paragraph together with this sentence; however, I decided to erase the paragraph. This little sentence, out of the context, was forgotten in the purge.
Dude in the back coughing would have the whole campus put into a quarantine tent 😂😂 in a 2021 lecture
Leonard susskind is amazing teacher
what an amazing lecture I'm sure that I'll study physics
Are you still in highschool?
yes in 10th grade
Did you study it?
@@AreebsStudyno, studying medicine now. but sometimes i miss physics a lot
1:43:00 The problem is ill-posed, "for its neighbors" should be replaced by "for the next coin". Otherwise, an outcome could influence the probability of the previous result which doesn't make sense.
It has bayesian sense I think
1:44:45 No. Boltzmann didn‘t mean that. This is the Gibbs entropy. Boltzmann and Gibbs entropy only coincide in equilibrium.
Mike, is that you?
just love the way you teach.
wouldn't log m emerge from integrating 1/m pieces as the total probability?
Statistical mechanics is not really modern physics, it is pre modern physics, it is modern physics and I assure you it will be post modern physics
Many thanks for sharing Susskind's vast knowledge.
May I ask what was the textbook the video learning?
My only confusion after watching this wonderful lecture is why are their only 4000 likes, from 400,000 views? SMH.
For those of you who are confused by the N(i)/N thing, and whether or not it goes to zero in the limit as n->infinity. Just keep in mind that N(i) is a function of N, and when N approaches infinity, infinity becomes a common factor and can be removed. You are left with a simple ratio. Consider a coin flip. N(i) will be 1/2*N. As N goes to infinity N(i)/N becomes 1/2N/N which reduces to 1/2 which is the probability of flipping heads or tails.
Sure is! Google L'hopitals rule.
As n -> infinity N(i)/N contains the factor infinity/infinity which is an indeterminate form. In the case of a coin flip it reduces to 1/2.
By common factor I meant that infinity is in the numerator and the denominator. You never actually get to infinity, but you can talk about limits as they approach infinity.
you are clueless dont type
❤beautiful lesson and demonstration.Thank you very much Professor and class
I only have one question.
How long is a short piece of string?
30min could you use this law to to predict how a virus evolves through an algorithm through the probability of its chromosomes configuration ?
That's only because the information about the past is now contained in the microscopic degrees of freedom of the ball and floor.
And you are not able to get at this information therefore your knowledge decreases and as a consequence the entropy increases, not because information is actually lost but because information is lost to you.
1:27:00 is it different when we know nothing about probability distribution than the case when we know that each state has same probability.? Even in first case the probability was taken uniform..
Absolutely wonderful
What are the prerequisites before taking this class? Should I know QM and thermodynamics like the back of my hand?
I think just Advanced Classical Mechanics and QM-1 is good enough?
On my uni course we did thermo and QM before Stats mech
If you know classical thermodynamics it's so much easier to understand. It's just a different perspective on the same concepts.
I have one very simple question.
According to this lesson, the probability P(i) = limit N(i)/N, when N approaches infinity.
If N(i) is not infinity, the limit of N(i)/N is zero whenever N approaches infinity.
What is the explanation of this probabilistic paradox?
This is why we use Probability Density Functions,
N(i) must go to infinity if N goes to infinity, unless the probability is exactly zero
Perhaps they approach infinity together, but at some fixed ratio to one another? For example, as the number of coin flips approached infinity, the number of heads results might also approach infinity, but at a rate half the total. I imagine N(heads) = N/2, so N(heads)/N = N/2N = 1/2.
He mentioned Liouville's theorem that states that phase volume is constant. But how is it compatible with entropy change? Entropy is increasing in general so phase volume should be increasing. But theorem says that it's not possible.
Very nicely explained. Easy to be good with such preparation and knowledge to impart.
What if the region in phase space collapsed into what would be a dirac delta function with the same area, but 0 momentum and an infinite number of possible positions?
"2 is the smallest integer that is not 1" -Leo Susskind
lovely lecture. very informative..
When he says the only way to ascertain the probability of occurrence when there are no clues is experiment. Actually there is a better way, a Bayes Way. You basically allot random probability and you update them with each experiment much more powerful than the frequentist way.
Which means you still depend on experiment.
He looks like someone who has mastered Physics before he even speaks, especially with that shirt. Sometimes we just need to listen to others, because what they say might be valuable.
I love his T-shirt.
Regarding the reversibility he discusses at 41:58: He says "you can not go back from red back to blue." [42:08] But is there not a certain probability of going "back from red" to a particular blue, similar in form to the predictability of rolling a die?
Notes of the lecture - www.lapasserelle.com/statistical_mechanics/lesson_1.pdf
mmm I found the example of the eraser and Liouville is a bit tricky. If the eraser has 20 molecules so the fase space has 40 dimensions. The initial state is that the position and momentum of each molecule has a uniform probability to lie in a certain subregion of a two dimensional subspace. It any of its molecules come to a rest (hard to imagine that they could do this separately but anyhow) it would mean that we are now certain that it stops, and Liouville theorem prevents that. It looks pretty much similar to the quantum mechanics situation. ?¿¿?
the eraser is not a closed system so I think you have to include the 20 molecules in the eraser and the molecules in the countertop that it interacts with. The ones in the countertop speed up.
great! absolutely loved it!
1:30:23 "2 is the smallest number which is not 1"
What a fantastic alecturing
'Two is the smallest number which is not one'
Dr. Leonard Susskind, 2013.
tyvm professor , very thorough but still easy to understand lecture
Very well explained, thank you.
Hey guys! Looks like there is a lot of courses on this channel, but it's complicated to navigate through them. Page with playlists of this channel - is it the only one navigation?
Visit the website of theoretical minimum - www.theoreticalminimum.com
Very nice presentation with good examples. Thank you for sharing.
bro they giving out this college stuff for free now??
Fantastic!
I have figured out how to extract the power of track in water to produce a thrust which in turns produces a lift for buoyancy. I cannot find a way to explain or celebrate my discovery.