The Misunderstood Nature of Entropy

Thank you - brilliant org for supporting PBS Digital Studios Entropy and the second law of thermodynamics have been credited with defining the arrow of time predicting the ultimate heat death of the universe and providing the driving force for the development of structure as well as decay and Also, excusing the messiness of your room, but what is entropy really and how fundamental is it to our universe? Entropy is surely one of the most intriguing and misunderstood concepts in all of physics the entropy of the universe Must always increase. So says the second law of thermodynamics. It's a law that seems emergent from deeper laws It's statistical in nature and yet may ultimately be more fundamental and unavoidable than any other law in physics Einstein said that the thermodynamics that encapsulates the second law is the only physical theory of universal content Which I am convinced will never be overthrown and the great astrophysicists or Arthur Eddington Warned if your theory is found to be against the second law of thermodynamics. I can give you no Hope there is nothing for it but to collapse in deepest humiliation We've looked at entropy in the past, but it's time to go much deeper to unravel the great unraveling Over some upcoming episodes. We'll explore different aspects and consequences of entropy Including its role in black hole thermodynamics and how it will lead to the end of our universe but today we'll see what entropy really is and why the second law of thermodynamics is considered to be so fundamental and so Unavoidable. Let's start from the beginning in 1824 Siddiqa, no published his reflections on the motive power of fire in which he revealed the theory for perfect engine efficiency Heat engines which in Connors day were the newfangled steam engines work by turning the flow of heat energy into mechanical energy for heat to flow you need two reservoirs of different temperature a Perfectly efficient engine one undergoing the Carnot cycle converts all transferred heat energy into useful work in Principle that work can then be converted back into heat? And so the temperature differential can be re-established However, an inefficient engine will slowly deplete the difference in temperature reducing the heat flow and the engine whines down Around a half century after Cano Rudolf Clausius was inspired to quantify this tendency of heat energies to decay over time Enter entropy Classiest define entropy as the internal property that changes as heat energy moves around within a system Specifically the change in entropy of each reservoir is the heat energy going into or out of that reservoir Divided by its temperature for a Carnot cycle the overall change in entropy is zero but for any less efficient cycle entropy increases in Fact an increase in entropy means that the heat reservoirs are approaching the same temperature Reducing the capacity to do useful work coño and Klaus uses were revealed entropy is a measure of how evenly spread out a systems energy is the more evenly spread the less useful the energy is and For an isolated system the best you can hope for is that the separation of energy and the entropy remain constant in? reality It will almost always increase unless energy comes in from the outside to reestablish the temperature differential This understanding of entropy is in terms of flowing Heat and it came from the days when many including Cano himself Belief that heat was a physical fluid called caloric. It took a revolution to understand the reality of entropy that Revolution was statistical mechanics founded by the great Ludwig Boltzmann with his kinetic theory of gases This theory explained thermodynamic behavior as the summed result of the individual motion of tiny particles under Newton's laws of motion Stat mech is really astounding it's founded on an absurdly simple idea for a given set of large-scale observable properties every Possible configuration of particles that could give those properties is equally likely Let's add some physics speak by configuration I mean the exact arrangement of positions velocities had said of all microscopic particles we call this the microstate and We call the specific combination of large-scale macroscopic properties The macro state macro states are entirely defined by thermodynamic properties temperature pressure volume and number of particles For a given macro state all microstates consistent with its thermodynamic properties are equally likely For some macro States there are lots of different microstates or arrangements of particles that lead to roughly the same Thermodynamic properties while other macro states can be produced by only very few Microstates. Ok, one more fact if you leave a system to do its own thing It'll eventually try out all possible microstates that are possible given the laws of physics All particle arrangements will eventually happen So if you look at the system at some random point in time It'll be in a completely random microstate chosen from all possible microstates And what macro state will have been well probably the one that's consistent with the most Microstates we can think of these micro and macro States with an analogy. This is a go board Let's say you place a hundred and eighty Blackstone's at random. Every possible specific arrangement is considered a microstate Well, the overall shape of the distribution would be the macro state there are nearly two times ten to the power of hundred and seven ways to arrange the pieces and Almost all of them are pretty evenly mixed So roughly all the same macro state some microstates are weird though And they give different macro states because they're different average distributions. For example, there's one Where all the stones are on one side? That microstate is a factor of two times ten to the power of one hundred seven less likely than one of the many smoothly mixed Microstates and the larger the board the less likely it is to end up in such a weird arrangement for a roomful of ten to the power of 26 molecules of air the chance of getting all of the air molecules on one side of the room by chance Is so small that it never happens. We've been talking a lot about particle position But really that go board is an analogy for all possible combinations of all property position momentum spin vibration really any degree of freedom that the system can have we call this space of properties a phase space and Instead of particles being distributed through position space a microstate is really defined by how energy is distributed through phase space the average distribution of individual particles in phase space defines the thermodynamic properties of the system That's why these similarly shaped distributions on the go board Correspond to the same macro state while the clustered spread does not okay so if you leave a system alone long enough, its Particles and its energy will find its way into all the different forms that are possible the vast majority of possible distributions of energy leave the system very close to a single macro state that's the state of thermal equilibrium in which Energy is maximally spread out and temperature pressure density volume, etc. Have the values we expect from classical thermodynamics? Statistical mechanics tells us why large-scale systems have the properties they do but what does this have to do with entropy? Well, Ludwig Boltzmann figured that out too the Boltzmann equation Tells us that entropy is the logarithm of the number of microstates Consistent with the current macro state times the Boltzmann constant So our smoothly spread our equilibrium go board has a high entropy and our clustered board has low entropy by the way There are certain special microstates special arrangements of particles that look highly ordered but are still Consistent with our high entropy macro state, for example, if we try to draw pictures or write words in phase space This is where we get to a point of common confusion Order is not the same thing as low entropy and the second law isn't always the tendency towards disorder in thermodynamic entropy the only special arrangements of particles that change entropy are the ones that change the Thermodynamic properties not the ones that spell out cuss words will mess up your room to get deeper into that We'll need to talk about information entropy which will also need for black hole thermodynamics And we'll take another episode Okay So the macro state that defines thermodynamic equilibrium is by definition the one with the most microstates Which also means the maximum entropy? Any system not in equilibrium must increase in entropy Simply because at any future time its current microstate will most likely be one of the more common types of microstate This is assuming you don't force the system from the outside And it's possible to take each ghost stone and place it on a particular spot to construct a special microstate or to use a vacuum Pump and a glass wall to move all of the air to one side of the room in both cases You are reducing the number of accessible microstates Which by definition must reduce entropy but to do so You must introduce an external source of energy Heat must flow between your system and the outside universe in a way that increases the entropy of the universe as a whole statistical mechanics Inevitably leads to entropy and the second law and it does so by something so fundamental and basic That it's impossible to deny. It comes from counting the ways that energy can be distributed The inevitability of the rise of entropy is as fundamental as counting That's why Einstein and Eddington were so sure of it, but entropy is also Statistical and emerges from the behavior of particles under the laws of motion This is where the second law appears to add something new to the universe Not seen in the more fundamental laws It seems to add the arrow of time See the laws of motion where the Newtonian or quantum mechanical don't care about the direction of time and yet the second law of thermodynamics Clearly distinguishes between the past and the future We talked a little about this in our episode on the physics of life Where we saw how entropy drives both the increase and decay of complexity It's almost like the concept of time is emergent and statistical just like entropy again We'll delve deeper into this in the future, but for now, please Be careful to keep your number of accessible microstates low avoid thermal equilibrium and keep being that brilliant macro state that is you until I see you next week on Space-time the field of statistical mechanics has given us some of the most profound insights into the working of both the large scale and quantum realms Stunningly its foundations are in probability theory to really get stat mech you have to get probability Brilliant org has a great course on probability that solidly founded on exercise based learning honestly, that's the only way to get math to do it check it out because we'll be doing more stat mech and delving deeper into entropy in the future Learning about physics is much more than facts and memorizing When done right it gives you a whole new way to look at the universe itself Brilliant math and science done right is proud to support space-time to learn more about brilliant. Go to brilliant org slash space-time

Channel: PBS Space Time

Views: 665,559

Rating: 4.9233103 out of 5

Keywords: thermodynamics, law, second, time, physics, entropy, pbs, space, einstein, boltzmann, statistical mechanics, stat mech, second law

Id: kfffy12uQ7g

Length: 12min 19sec (739 seconds)

Published: Wed Jul 18 2018

Reddit Comments

[u/JackieMittoo]

Fantastic Show

[u/Tablecork]

This really helped connect a few things I didn't understand!

[u/Canned_Moose_8]

The end had one of my favorite lines on why I love physics. It deepens the understanding of the universe.

[u/EquinoxEventHorizon]

Thank you for this.

[u/Suddenbagel]

Man what a brilliantly produced video! Cheers :)

[u/PapaTua]

PBS Space Time it generally excellent and Matt O'dowd is a fantastic presenter.

[u/dialecticwizard]

Thankyou. One area I need to bone up on.

[u/68024]

Time remains one of the most elusive aspects...

[u/rousbound]

Saving!