The second law of thermodynamics addresses the necessity of entropy and the limit to which an equilibrium condition at a given temperature can be achieved, and the necessity to have a low temperature reservoir to reject energy into in order to achieve an equilibrium state. The third law of thermodynamics is really just a consequence of the second lw, i.e. that entropy becomes a constant as the system approaches the (global or ultimate) low temperature reservoir. In other words, all it really says is that to achieve an arbitrary low temperature, the entropy of any subset of your global system can’t be any more than the average entropy of the entire system. This also means that absolute zero, in thermodynamic terms, is impossible to achieve as long as your system has any energy in it whatsoever. If you actually had a zero energy outlet you would have a perpetual motion device by virtue of having infinite energy flow (infinite to the extend of all of the energy in the rest of your universe).
At any rate, no principle of thermodynamics as currently formulated is dependant upon quantum mechanics, and most common formulations of quantum field theory (or at least quantum electrodynamics) are time symmetric, and thus, don’t support the second or third laws of thermodynamics as conventionally stated. Classical equilibrium thermodynamics are solveable in closed form assuming continuous differentiable and integral functions. Generalized thermodynamics–the heat transfer mechanism occuring in non-equlibrium states–do require statistical mechanics and for certain fundamental types of phenomena, such as conversion from radiation to internal motion (heat), also require quantizing the system in terms of discrete energy transfer between categories of individual ‘particles’ (atoms or molecules with specific energy levels and degrees of freedom) but this doesn’t require delving into the bizarreness of quantum mechanics; it just assumes that energies and degrees of freedom occur along a defined distribution depending on the types of particles and the temperature of the system. While some of the phenomena arising from investigations of statistical mechanics led to the theories of quantum mechanics at a fundamental level, statistical mechanics itself is still a quasi-classical theory, and models from it reduce to classical thermodynamics as you approach equilibirum conditions.
General relativity is a geometric theory of gravitation and has (at this point) no clear relationship to thermodynamics insofar as the priciples of thermodynamics are not required to explain any observed phenomena, and in fact are only applicable in very exotic conditions, e.g. at the event horizon of a black hole or gravitational interactions between two supermassive corotating objects, that we have never directly observed. We don’t see the orbits of planets decaying because of radiation losses from gravitational exchanges. There is a hypothesis called entropic gravity that posits that the force we observe as gravitation and interpret as a curvature of the underlying plenum of spacetime is actually an emergent result of the consequence of the distribution of mass-energy coming to equilibrium, but at this point it provides no testable phenomena that are distinguishable from general relativity and so is only interesting.
Gravity as an emergent property rather than intrinsic, you say? That does sound intriguing. Gonna have to read up on entropic gravity.
Frame-dragging (measured at 42 milliseconds of angle per year by Gravity Probe B) does transfer energy from the Earth’s rotation to the local space time plenum doesn’t it?
Does it? I always understood the plenum itself to be agnostic to distortion, that energy can only be transferred between mass-endowed entities within it. Gravity itself is a potential, like voltage.
Energy can be carried away via gravitational waves, even if it’s ultimately never carried to any other object or system. There are some subtle mysteries about just where and how the energy is present in a gravitational wave, but it’s definitely there somehow.
Regarding the uncertainty principle and absolute zero.
The product of uncertainty of momentum and uncertainty of position is a constant.
If a particle (regardless of uncertainty of mass) was not moving, it’s momentum would be exactly zero, ergo the uncertainty of momentum would be zero. That would imply that the uncertainty of position is … not defined. (As you approached zero momentum the uncertainty of position would grow towards infinity. I.e., the particle could be basically anywhere.)
Ergo, no real particle can stop moving.
It is a consequence of thermodynamics that the effort to approach absolute zero is exponential. I.e., it is just as “hard” (in some sense) to go from 8K to 4K, from 4k to 2K, from 2K to 1K, etc. Achilles can’t really catch the tortoise.
Throw in vacuum energy, etc., and the classic view of absolute zero meaning no motion is just a simplification with no real application.
In answer to the OP: there is no direct link between time and thermodynamic temperature in GR.
One area where the 3rd law of thermodynamics and general relativity collide in an interesting way is in black hole thermodynamics. The third law of black hole thermodynamics means that it is impossible to create an extremal black hole (e.g. a Kerr black hole that is spinning so fast it has no event horizon).
There is a relation between temperature and the gravitational potential, though, known as the Tolman-Ehrenfest effect, where (roughly) a fluid column will be hotter at the bottom by some 1/c^2 correction; that is, in GR, temperature is no longer constant in equilibrium. Thus, GR does have some effect on thermodynamics; however, a fully general relativistic thermodynamics is still an open problem.
Think of it this way. In thermodynamics, how do you cool something down? You put it in contact with something at a lower temperature. However, by doing so, you’ll slightly heat up that colder thing, so the two objects come to an equilibrium temperature somewhere in between. So how would you cool something down to absolute 0? You’d need an object that’s colder than 0 so they could both come to an equilibrium temperature of 0. And there’s nothing colder than 0.
Well, that’s the simplest way to cool things, but it’s not the only way, or refrigerators and air conditioners wouldn’t work. Still, all those other methods have their own reasons why they can’t reach zero.
Good point. Is there a word used in thermodynamics , in the largest sense, of cooling in the AC way versus the other ways?
And I’m understanding your reference to AC/refrigerants in the only way I can, as a Carnot cycle. If that is what makes the difference, I still don’t understand what makes it so.
So, in Thermo 101, what are the typologies of cooling?
I don’t know about current extreme cooling methods, but one method used decades ago used semi-magnetic particles in He solution.
You applied a magnetic field, cooled the stuff the best way you knew how, removed the magnetic field. The change in phase of particles as they became unaligned drew heat out of the He and you got a burst of chilling. This could be repeated/cascaded a bit to chill even more.
A quick Google turned up a few things, some with words I sort of understood.
The curious ones were: temperature = speed of time. Where there was a notion of thermodynamic time as opposed to mechanical time. Here, curiously for the OP, it seems that the hotter things are, the slower time runs.
The information content notion of entropy would seen to intuitively make sense here, as for time to run you need to change the state of the system.
One suspects there might be something very deep here, but I’m not quite sure what it might be.
Well, you and me both, and hence, I didn’t comment on it. I’ve had a look at the issue some time back, but never got in deep enough to feel qualified to comment; so let’s just say that at least at the moment, this is an extremely speculative proposal with somewhat uncertain status.