leonard susskind statistical mechanics

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Leonard Susskind is the Felix Bloch professor of Theoretical physics at Stanford University. He begins with a brief review of probability theory, and then presents the concepts of entropy and conservation of information. Statistical Mechanics (Spring 2009, Stanford Univ.). Lecture 1 | Modern Physics: Statistical Mechanics - YouTube Statistical mechanics is a branch of physics that applies (Source: Wikipedia). Statistical mechanics provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic bulk properties of materials that can be observed in everyday life. Leonard Susskind explains how to calculate and define pressure, explores the formulas some of applications of Helmholtz free energy, and discusses the importance of the partition function. Statistical mechanics provides Thus it explains thermodynamics as a result of the classical and quantum-mechanical descriptions of statistics and mechanics at the microscopic level. In this final lecture, Leonard Susskind covers such topics as inflation, adiabatic transformation and thermal radaition. All Rights Reserved. Please log in in order to save this video to your watchlist. Thus it explains thermodynamics as a result of the classical and quantum-mechanical descriptions of statistics and mechanics at the microscopic level. Leonard Susskind presents the mathematical definition of pressure using the Helmholtz free energy, and then derives the famous equation of state for an ideal gas: pV = NkT. This website uses cookies to ensure you get the best experience on our website. Leonard Susskind discusses the study of statistical analysis as calculating the probability of things subject to the constraints of a conserved quantity. Leonard Susskind picks up on magnets, phase transitions, and mean field transitions. Leonard Susskind discusses the basic physics of the diatomic molecule and why you don't have to worry about its structure at low temperature. Statistical Mechanics (Spring 2009, Stanford Univ. a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic bulk properties of materials that can be observed in His research interests include string theory, quantum field theory, quantum statistical mechanics … Statistical mechanics provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic bulk properties of materials that can be observed in everyday life. (April 1, 2013) Susskind introduces energy, entropy, temperature, and phase states as they relate directly to... Leonard Susskind overviews elementary mathematics to define a method for understanding statistical mechanics. S by a go-ahead here with those of a rumor that the E by T. right Daddy but please Tobias by also accounts volume OK so here I had my D E baby AS Carson volume all with still 1 more thing now sorry we're interested in the rate of change of EU with respect to beat that means we should the by built the Treaty on both sides to see get rid of the dope be provided by Dr. provided by Delta OK so now we're Kirgan but where so far have I put in that I've moved along the line of constant XI I have nothing in here has told me that I'm moving all along the line from 1 point to another, along the lines of constant entropy know why wouldn't arrested in country comes entropy will come out not from this formula but will come out soon enough so but a case so will move along this line how comely characterizes like this curve because point is characterized by slow that's the is just it he by Delta Street let's see what we can figure out of our let's is a little bit of a calculus to see if we can work out something about the tea by Delta we let's write down a conditional moving on a line of constant attacks that is along this line DES is equal to 0 along this line PS is equal to 0 and now we have to do is write the DES partial other s with respect volume at 6 p trends volume Delta Force the volume plus partial of S with respect tea at fixed volume has dealt take boasts learning VS is equal to 0 0 right yes is equal to 0 along with the definition of a line of would make this equal to 0 and now they be able to get a formula Fidel the T by Delta V in terms of these partial derivatives to going abide by Dr. B. because we want to stoke the by dose of solids the vibe don't think Hey we have our target of India delta of the tea by Dr. B. we can now immediately read off that Delta T size dealt the VAT is equal minus D S by V at constant TV divided by U.S. did TD at constant V this would be true for any function tests whatever on this map year that the slope of we can't lines the slope of the contour lines is related to certain partial derivatives had a off I would at that takes me and the move to see why this is I have to go through this will step you see but now we know what Delta T by Delta so let's put it that 1st of all gives us a minus sign and then delta T by Delta V partial that's what's right about partial abreast with respect to V a Council but he can't provided by a partial rests with respect to at constant as array of 4 factors in 4 factors 3 in the numerator 1 in the denominator this is in the denominator devoted VS beauty but foot cynically by a great stroke of luck that thing in the nominator happens to be the same thing as 1 of the terms enumerator get I said we could've gone off in all sorts of random directions but this taxes in there but warned because this is getting simpler now so let's get rid of the numerator sorry made and the numerous Ada I would not what done where we deliver we done believe we've proved this little limit yeah I cannot fill slimmer without drawing his picture it's something you wanna be able approved displayed mechanical steps but I cannot rule out during pictures and they're figuring out warm doing says a sure it said that there is no doubt that arm for most systems in most circumstances yet there are some special cases were much rule and then you have to be more careful but generally speaking yet Bancorp is a monotonic function of temperature and the reason is the reason is simple love the Boltzmann distribution as you see the temperature if you increase the temperature it gets narrower his you decrease the temperature it gives broader and entropy is just a measure of that with sold typically yes some very special cases but but yacht are your of things are nicely behaved OK so here we have our 2 facts the 3rd factor has to do with the definition of pressure end I want to make very clear that pressure just 1 special case of 80 responds to a control parameter were by response control prime solve hours because they want 1 act 1 thing we have to do but actually tools but they're easy firstly understand what pressure really years here's are still under his arm pistons molecules in here hitting the Pistons so for exerting pressure on it supposing we move the piston a little bit maybe pressure in the interior does work on the press only our on to the promoters and how the pressure pushes out and those who work on that work winners at work come from that workers energy the work done on the past and is equal to the change an opposite sign if they have to guess does work on the Pistons then there's a change in the energy in here on negative think they work maybe they get smarter but a brought the following way and they think about a, thief Nagin the piston rises a little bit wealth that means there's been an increase and energy in and the gravitational potential energy of the and in this case that's called the work done on the piston by but pressure and by energy conservation any work would start on the Pistons must be taken away from me you from the gaps to energy conservation tells us that we change in energy of the gas is minus the work done on the piston now let's suppose that area of the piston is but suppose the piston is moved by an unknown DX vertically DX vertically and let's and you also have to imagine something else we have to imagine 1st of all that we do this slowly arms some odd things can happen if you do it fast for example you Coppola piston out so fast that no molecule has a chance to hit the distant as is moving the knowing that had been no pressure are OK that's a rather extreme situation but it does illustrate for you that you want to define pressure by being able that average over many collision was so you want to slowly move the piston slowly slow motion and no limit of very slow motion and the something else you wanna do you wanna make sure no energy comes into the system from outside no would you want to insulate the walls of the system I remember when I was a undergraduate I learned the word adiabatic I had no idea what it my professor of engineering told me that there needs that a system is insulated From he coming into Iraq and later on when I was in graduate school another professor from me adiabatic means slowly well what abatic means is slowly and no he comes at the if you move the piston 80 directly with no heat coming into the system change of the energy of the gas is minus the work done on the Tristan and miners who worked on the testing is before my is a force on the distant pressure area pressure times area of forest pressure times areas faucets definition of pressure force per unit area force harms, DX ART at times DX is the change in the volume of the gets right area times DX is the change in the volume so we can write a DX as DVD now that this is away and Mr. Farley's pressure you can make it defines pressure we in fact is where we go right we can write if that is the change in energy with respect the volume the only question is whether we keep fixed in doing this derivative where we keep fix some rate of change of energy with respect the volume under the circumstances that we do the operation AT about equity OK now was another aspect of the notion of 80 abatic anybody know another Nova meaning Tati batik for the 2nd law of thermodynamics which will come to says entropy always increases except for about where doesn't increase it stays the same never decreases never say never but never Mark OK 1 up process to use with the entropy doesn't increase stays the same Bozo the 80 batik, 1 so let me explain to you I'm going to explain it to you from a quantum mechanical point of view we would land the only aspect will use of car mechanics is energy levels of discrete nothing else no words easily ART Sebire definite energy levels so we cannot box of gas at a resort and here I'm going the plot the energy levels as a collection of energy levels above collection of possible energies that the gas in the box can have not the single-particle energy levels the possible energies of everything inside the box there's some discreet collection of numbers in quantum mechanics in any case now would achieve the volume chain of Are you and what happens to the energy levels they stay the same why should your account energy levels after solve some problems loading or equation whatever the Schroedinger equation depends on the size of the box and the energy levels change our factor that right upside down as you increase the volume of a boxy individual energy level surely go down but it doesn't matter because there were just being General we got a magic situation will be energy levels go up at the present time 1 is notices is something that I'm not going to prove to you it's a quantum mechanical theory called the idiomatic beer I want says is that the system has a definite energy and use slowly change the permit this case of volume whatever control parameter happens to be if you slowly change it the system was steady and simply ride along the energy level keeping not the same energy but it won't jump from 1 energy level for another it will simply steady if it's if this is the 500 thousand 37 energy level the system will stay in the 537 wherever I said whether the numbers of the energy levels will be remembered and started again it will be yet and he changes system rapidly this is not what happens to change a system rapidly you could have jumps from 1 you level to another that's what's special about 80 back if you go slowly the energy levels entered the value will be energy changes slowly but you don't jump from 1 to another that means if you started out with a collection of probabilities piece of art labeling video of the probabilities for different energy levels the peso by stay the same the value of energy Musharraf but the probabilities don't change if the was a probability that say Zero everywhere except for this particular energy level you'll still have 0 everywhere as except for the energy level here if you have a probability half year and a half he had it will remain a half half so wildly trying the peace Andy entropy is just bill from the peace of mind doesn't care what energies are you have a probability distribution then is equal from minus some additional I piece of I want peace of mind and a faux probabilities stay the same thing you conditioner entropy stasis and that is why & AT & batik processes also sometimes called an isentropic process mean to say that the entropy doesn't change that the general definition of 80 about no change in entropy now of course slow would not be good enough if you could put heating of the system put he'd into the system that's that's corrupting it and a changing the system change in the energy about which 1 do AT abatic means slow with Norway added or subtracted heat and under those circumstances idiomatic also means constant entropy so now we know what the whole fixed in this formula change and the energy with respect volume holding me entropy fix while that of course is the reason that I went Bender but the reason we spent time California of are this thought it was good enough but it's kind of hard to calculate things affixed entropy you have to figure out what do what you usually provided with the easy thing to to calculate is things it's fixed temperature you stick in the temperature in the Boltzmann distribution you calculator would you get out cancer which depends on the temperature be easy thing usually to calculate how things vary with temperature just because you temperature a thing which directly appears distribution here so it's always easier to more as a function of temperature than as a function of anything else so would like to do is to convert this is something that involves derivatives With respect 2 temperature instead of entropy and then we can go back and see what we tumor from from the Boltzmann distribution OK so he'll have this is equal to the river energy with respect for the volume act fixed temperature other words holding fix the temperature and the Boltzmann distribution my U.S. a rewrite Landis a, derivative of entropy with respect for the volume at a fixed temperature of times the derivative on the energy With respect and be have fixed while you that this looks terrible looks too complicated but fortunately this is something we seen before but remember would Debye DES is the temperature holding the volume text holding the volume fixed media holding the system fixture not changing the control parameters it's just the original system with fixed energy levels and your holding that fixed under those circumstances D E by D S it is just the temperatures and that's D E equals TBS illegals or large P E by S is the temperature so this is not quite so bad we could replace this factor over here just by the temperature it's getting simpler for I the now yep Ferdie yes but catch but thank you copy now the, only derivatives are derivatives with respect the volume of fixed temperature that some promising volume and temperature commit lovers independent variables and the only the reviews of Pierre are so familiar things how the energy changes with respect the volume at fixed temperature and how s changes with respect the volume and fixed temperature T as just a temperature 1 more step because also happens to equal might the derivative with respect to the volume at fixed temperature of energy my tee times yes I'll take the 1st considered by DVD that's devalued by via fixed temperature the 2nd terms if I differentiated with respect the volume fixed temperature I would get 2 terms from a product here 1 of them would be he times a derivative of vest with respect to a volume at this 1 what's the other 1 the other 1 is derivative will respect the volume of the temperature at fixed temperature how the temperature changes you very the volume if you keep the temperature picks it doesn't change right so the 2nd terms there a smell we have are fundamental theorem pressure is equal to the derivative with respect to the value of the Helmholtz free energy at a fixed temperature now that is much simpler than anything else you could emerge from pressure and in fact we know more we know that they Helmholtz free energy is just minus logs easily calculated them partition function was sort of finished so let's that again think its class members with plus plus the derivative with respect to a volume is fixed temperature so we can take the temperature army outside works with only the plus sign the temperature times derivative of log z with respect of volume came at a fixed temperature always need to be able a calculator is how the partition function depends on the volume and we can calculate the pressure everything I've done up till now is completely general it wouldn't matter if were liquidated against up plasma lover or a solid solid inside the cylinder it doesn't matter what the chemical composition is this is what statistical mechanics not not Connecticut Peri kinetic theory resistant to picture of molecule bouncing around this newest statistical mechanics says pressure is equal to temperature at times and delivered derivative of the partition function now you can calculate the you tell you this Our would for it basically any control parameter I just use volume as a control parameter because of familiar to any control parameter there is always a derivative of energy with respect to the control parameter at fixed entropy that is called the conjugate thermodynamical variable volley of volume and pressure are conjugate variables thermodynamically many others lack of going to the now about any kind of a control parameter then you could ask how the energy of the system depends on a control parameter fixed entropy and that the fines and another variable which is like pressure which plays the role of pressure type of let's that's now we've Lilly fast so I thought because we don't want hire and annuities were, want 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