Open Thread, Feb. 2 - Feb 8, 2015

Gondolinian

If it's worth saying, but not worth its own post (even in Discussion), then it goes here.

Notes for future OT posters:

1. Please add the 'open_thread' tag.

2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)

3. Open Threads should be posted in Discussion, and not Main.

4. Open Threads should start on Monday, and end on Sunday.

If it's worth saying, but not worth its own post (even in Discussion), then it goes here.

Previous Open Thread

Notes for future OT posters:

1. Please add the 'open_thread' tag.

2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)

3. Open Threads should be posted in Discussion, and not Main.

4. Open Threads should start on Monday, and end on Sunday.

In a previous thread, I brought up the subject of entropy being subjective and got a lot of interesting responses. One point of contention was that if you know the positions and velocities of all the molecules in a hot cup of tea, then its temperature is actually at absolute zero (!). I realized that the explanation of this in usual terms is a bit clumsy and awkward. I'm thinking maybe if this could be explained in terms of reversible operations on strings of bits (abstracting away from molecules and any solid physical grounding), it might be easier to precisely see why this is the case. In other words, I'm looking for a dynamical systems interpretation of this idea. I googled a bit but couldn't find any accessible material on this. There's a book about dynamical systems approaches to thermodynamics but it's extremely heavy and does not seem to have been reviewed in any detail so I'm not even sure of the validity of the arguments. Anyone know of any accessible materials on ideas like this?

The lesson is that statistical methods are superfluous if you know everything with certainty. It's worth noting that classical mechanics is completely symmetric with respect to time (does not have a distinguished "arrow of time"), whereas thermodynamics has a definite arrow of time. You run into problems if you assume that everything behaves classically and try to apply thermodynamic notions.

Landau and Lifshitz's Statistical Physics has some discussion of issues with entropy.

4mwengler11y

At least if you are talking about Physics, whether you know the position and velocity of every atom in a system or not is irrelevant to what its temperature is. The point of thermodynamics is that under a broad range of conditions, there are statistical quantities which are predictable, such as the average kinetic energy of components after "enough" time has passed (enough time to reach thermal equilibrium in a given experiment),and of course it is not only the average kinetic energy, but the distribution of energies which are known. There may be interesting or even amusing information theoretic senses in which tracking the microscopic details can be said to have zero entropy, but these do not impact the physics of the system. IF the system is one in which the conditions for thermal equilibrium being reached are there, then we will be able to predict the same distribution of kinetic energies in the system whether or not we are tracking every single molecules velocities and positions, or not. As to whether or not a 0 K ice cube will melt, it will melt if your put it in contact with a gas that has enough kinetic energy in it such that when that energy is divided by all the molecules in the system, the average energy per molecule is greater than k*274 K where k is boltzmann's constant. Your detailed knowledge of every molecules position and velocity will not stop the ice cube from transitioning to its liquid state as kinetic energy from the gas is transferred into the ice cube. NO matter how entertaining alternative definitions of entropy and temperature might be, they are completely irrelevant to the time-evolution of liquids, gases, and solids interacting under the conditions in which they are described to good accuracy by thermodynamics. There is nothing arbitrary or "in the mind' about thermodynamics, it is a simplified map of a large range of real situations, a map whos accuracy is not affected by having additional knowledge of the terrain being mapped.

10Pfft11y

Isn't all this just punning on definitions? If the particle velocities in a gas are Maxwell-Boltzmann distributed for some parameter T, we can say that the gas has "Maxwell-Boltzmann temperature T". Then there is a separate Jaynes-style definition about "temperature" in terms of the knowledge someone has about the gas. If all you know is that the velocities follow a certain distribution, then the two definitions coincide. But if you happen to know more about it, it is still the case that almost all interesting properties follow from the coarse-grained velocity distribution (the gas will still melt icecubes and so on), so rather than saying that it has zero temperature, should we not just note that the information-based definition no longer captures the ordinary notion of temperate?