You knew this one was coming, right? Why the past is different from the future, and why we seem to flow through time. Also a bit about how different groups of scientists use the idea of “information” in very different ways.
The Biggest Ideas in the Universe | 20. Entropy and Information
And here is the associated Q&A video:
The Biggest Ideas in the Universe | Q&A 20 - Entropy and Information
Very interesting video, thanks!
But (like, it seems, many others), I’m still a bit confused about the relationship between the physical world, and information. Take for example Maxwell’s demon. How does the deletion of information of the demon affect the state of the molecules in the box? Or, if it doesn’t affect the state of the molecules, how is it relevant?
Is more chaos the same thing as higher entropy? Also, the concept of entropy is starting to look to be less about physics and more about awareness. Am I wrong to think that way?
Hi Sean,
Thanks for the great video. I have a couple questions:
– can you explain how to get from the past hypothesis to dS/dt>0? Naively, I see that it shows entropy should have increased on average since the beginning of time, but not that it would have increased at every t. To put it another way, what does the cup of coffee and milk has to do with the beginning of the universe, at least for small dt?
– you mention it in something deeply hidden, can you expand on the idea that the (most probable) irreversibility of wave functions decoherence have to do with the (similarly most probable) irreversibility of increasing entropy?
Does collapse (or branching) of the wave-function has anything to do with the foundations of the arrow of time? Meaning, the reduction of the state vector *is the thing* that makes physical processes irreversible?
Thanks, professor Carroll.
Me again, and my question about Maxwell’s Demon, and the relation between information and energy evolved again.
After discussing on youtube, now I understand that the amount of energy dissipated on the Demon’s memory-erasure takes into account the surrounding heat bath’s temperature, and the released energy is kT ln(2) per bit info, and this is Landauer’s principle.
However I found that Landauer’s principle is incompatible with the First law of thermodynamics (law of conservation of energy).
Let’s examine the experiment from the point of view of energy conservation, where energy conservation is prioritised over Landauer’s principle.
This time is suffice just one box, with it’s particles in thermal equilibrium with it’s surrounding heat bath.
The total energy of the heat bath, the box, the released energy on erasure, and the eventually extracted energy from the heath bath has to be constant all the time.
Let the Demon do it’s action, and after a while evaluate the energies:
Case 1.) The box is now in some non-thermal equilibrium, but no energy extracted, and ask the Demon now to erase it’s memory. Obviously at this point no heat is missing from the heat bath, we started the experiment at thermal equilibrium, and the action of the Demon doesn’t change the energies of the particles/molecules (that’s the point)
So the heat bath’s temperature is the full-initial temperature and on memory erasure suppose to release kT ln(2) per bit info heat. Which is wrong, since this would create energy over our total (so far unchanged) energy.
Case 2.) The box is also in some non-thermal equilibrium, also no energy extracted, but this time open the box’s separation wall, and let the left and right side to return to thermal equilibrium, but in the meantime the Demon also keeps the information. When done, the whole setup is in thermal equilibrium, no energy extracted, but the Demon has some information, which we ask now to erase. According to the heat bath’s temperature kT ln(2) amount per bit of heat suppose to dissipate the Demon’s memory. Again wrong, energy would be created in this way.
Any ideas to solve the energy-paradox?
Agree with the Boltzmann Brain comments – it’s seems like given the laws of the universe, a tiny fluctuation in entropy the early state of the universe that results in a slightly denser region of matter that deterministically collapses into a stellar system in which life evolves over billions of years is much more likely than a brain randomly fluctuating into existence in the void
Doesn’t the thermodynamic definition of entropy imply coarse graining based on energy?
(So do the other definitions suggest other useful quantities analogous to temperature?)