sethoflagos

It's late and a combination of your obscurantism and swansont's bloody-minded negativity has exhausted my patience (which to be frank, I've never had in great excess). It must be obvious to you by now that I've been clear in my own mind since way back on page 1 of this thread where the Youtube presentations break down. The key lies in conservation of angular momentum which is a topic I usually shy away from. Turns out, it can be quite useful on occasion. Do we have anything more to discuss? If your earlier posting was a joke, then I'm sorry I didn't get it and took its meaning at face value.

I'm sorry that the standard engineering techniques for analysing thermodynamic systems cause you such consternation. Better engineers than me have approved my approach and given me repeat contracts to lead the detailing out their power design projects since I turned thirty, and that was a very long time ago. Your pride blinds you. I'm out of here. Just stick a heat engine between T2 and T1 heat reservoirs and you've got free energy. Well done! You've solved the worlds energy problems! Have a ball!

Do you think this is the first time I've ever seen a sketch for a heat pump that claims to break the 2nd Law? Really? I've just worked through the expression for the shaft work of your blasted adiabatic compression stage wondering why the hell am I spending my time on this hair-brained stuff when I'm not being paid for it, and you have the gall to say I'm messing around wasting everyone's time. HOW DARE YOU! Let's be clear on this - you are the one who has come up with an invention that any patent office would chuck in the waste-paper basket unread! I had about 12 hours work left to properly research and analyse your scheme so that I could help you through your misunderstanding. I've been helping my junior engineers overcome such hurdles for many years. But now shall I bother? What the hell do you think. Grow up!

I've not changed the conditions one iota. Even ideal systems have to observe basic symmetries. Better. Now sum all those microstates where the container remains unchanged from its original state, and we have a workable thermodynamic ensemble. The mean free path in air is what? 100 nm? There may be a lag between arrival and collision, but it's trivial in a macroscopic system. We don't need a 1-1 match up. The entire reaction vector to the momentum of a single particle can be split anyway you like between the remaining N-1 particles in the system. In a sense it is. So long as motion of one particle is exactly matched by some ensemble in contrary motion to fill the void, then sanity is preserved and you have the restoring force you've been asking for. Not when you've transferred nett momentum into your box. But now you have a non-canonical microstate. Do you really think you can both have your cake and eat it? They all require work in a sense. However small fluctuations are reversed almost immediately by the inertial reaction mechanisms discussed above, and are inherently reversible in nature. Larger fluctuations imply a long term resistance to those reaction forces that increase in direct proportion to the scale of the disturbance and I see no internal mechanism that could account for such a resistance.

Looks to me like you've just heated up some high pressure gas from T1 to T2 at roughly constant pressure. Close the cycle, put some preliminary numbers to it and we can discuss.

However all the particles are in one side of the box. So lets drop in a partition isolating a system of N particles on one side from an absolute vacuum on the other. Please don't reply 'there is no partition'. Yes it is. Ball and box is a two-body system with regular interchange of (at the very least) momentum between them. If you think that this is awkward, just wait until we start considering the regular interchange of torque. Every action has an equal and opposite reaction. Every particle arrival or departure within a space brings with it changes in mass, linear momentum, orbital angular momentum, axial spin etc and each must be balanced precisely by an equal and opposite external action. Sit it stationary at the CoM and forget about it. It isn't a problem until something bumps into it. I'll ask the mice. The box is a mathematical artefact introduced solely to define the system geometrical constraints. A condition of it being considered non-interacting is that we must be able to delete it from the snapshot and see no nett change to the system. Therefore the only states it is admissible to consider are those where every single particle linear momentum vector is exactly balanced by an equal and opposite vector. Just as the box could transfer momentum to and from the system, so can the octants transfer momentum between each other. While it must be possible for one octant to momentarily grab an extra particle or two (I'll agree with you that far), there are one or two particles on the imminent verge of leaving it probability one ensuring that the system never departs by a measurable amount from equilibrium. Serious departures demand serious external work.

Every fibre of my being feels this principle to be true. Though the name is unfamiliar to me. Thank you. I'll try to remember the spelling! Fire away, I'm all ears.

The 2nd Law is the 2nd Law. Let us assume dS/dt >= 0 for an isolated system. You're in the same trap as swansont. At each bounce, there is an interchange of momentum with the box. The box is actively participating in the thermodynamic process, so you now have to consider it's inertia, thermal capacity, temperature and entropy. Your system is an almost perfect vacuum. You want to discuss vacuums? They're pretty well defined, I think. It's rapidly becoming irrelevant in your idealised case. I'm more interested at this point in what the temperature of your box is, since this is now setting the conditions necessary for thermal equilibrium. Is it? Never heard of it. Your box is an active part of the thermodynamic system, which is why I ask what its temperature is, because that will define the equilibrium state. I suspect with only one single particle the equilibrium temperature is to all intents and purposes absolute zero, so your particle will shed its last little shred of momentum to the box and become stationary wrt the system CoM. Equilibrium has been reached. Real world processes tend to follow non-analytic PVT paths, which is why we characterise them by a sequence of analytic ideal steps, often an infinite number. There may well be no physical piston or heat exchanger involved but is entirely appropriate to fabricate a few for calculation purposes. See https://en.wikipedia.org/wiki/Thermodynamic_process_path#:~:text=A thermodynamic process path is,-entropy (T-s) diagrams. "A thermodynamic process path is the path or series of states through which a system passes from an initial equilibrium state to a final equilibrium state and can be viewed graphically on a pressure-volume (P-V), pressure-temperature (P-T), and temperature-entropy (T-s) diagrams. There are an infinite number of possible paths from an initial point to an end point in a process. In many cases the path matters, however, changes in the thermodynamic properties depend only on the initial and final states and not upon the path." At last! Conservation of linear momentum. It's not permissible in this simple NVE case to conveniently transfer some to the box because that is the equivalent of introducing external Q and W terms. Precisely! A low one. You objected to my earlier suggestion of 42, but it wasn't entirely flippant. Enough to constitute a system that isn't too swamped by quantum effects. Having said that, if you take the st. dev. of momentum from the Maxwell-Boltzmann distribution and plug it into the Heisenberg Inequality, some very interesting expressions arise that look very 2nd Law-ish to me. I suspect a very deep link in there somewhere, which actually strongly enforces my trust in the 2nd Law.

No, the CoM of the ball (wrt the system CoM) is not fixed. It was you who introduced the single ball case Needlessly offensive phrasing. My 'agenda' is simply to respond to points you raise in support of arbitrary random changes of state. There's a principle we use in Chem Eng that the transition between any two thermodynamic states is path independent i.e. when a body of gas transforms from one PVT state to a new PVT state, it is perfectly admissible to break it down into a sequence of smaller idealised steps, knowing that the overall changes remain fixed for purposes of calculating the enthalpy changes for instance. Hence, in the case in question, I analyse the change as an ideal isentropic compression (external work performed with no change in entropy) followed by a possible reversible cooling stage (shedding heat and entropy into the environment). The Youtube presenters haven't specified the final temperature of the system, but they have stated that the entropy has fallen, therefore the cooling stage is a valid means of estimating the minimum transfer of entropy. My 40 years work experience screams out 'THE ENTROPY OF THE ENVIRONMENT HAS RISEN BY AT LEAST AN EQUAL AMOUNT'. Must have. Otherwise all my design calculations over the last 40 years have been wrong and numerous production facilities around the world are fundamentally unsafe. A little over-dramatic maybe, but my hackles have been raised.

I do not believe it is possible for all particles to be on one side of the box in the absence of shaftwork or equivalent energy input. We're not able to compute system evolution collision by collision, but what we do know for sure is that the outcomes of each collision are very far from random - the entire discipline of physics is based on the symmetries of conserved quantities through such events. That deterministic principle does not suddenly vanish simply because we have insufficient computing power to handle the long term dynamics of macroscopic systems: those single event symmetries remain intact, instant by instant, eon by eon. In my experience, truly random behaviour is rarely observed and then only in a very few, very special scenarios. The rest is merely 'complicated'.

The overall CoM is essentially fixed by your constraint of infinite box mass. The total linear momentum of the system with respect to the total CoM is equal to the linear momentum of the ball wrt the total CoM. What happens at collision with the box wall is observer dependent. An observer travelling with the ball will see the ball suddenly accelerate from rest and deduce that work has been done on the ball providing it with a kinetic energy it did not previously have. An observer stationary wrt the system CoM may (per your assumption) see a specular collision where the kinetic energy of the ball is preserved. A third observer may well see the ball suddenly come to a standstill. All intermediate variations are possible. Single particle thermodynamics really has no meaning due to this observer bias. It isn't until we get into multiple particle systems where particle-particle collisions are possible, that we can shake off this observer bias and establish the concept of thermodynamic equilibrium - one requirement of which will be to set constraints on the motion of the centre of mass of the particles in the system (excluding the box). Maybe I should give you a heads up of where we are heading with this. I'm using a combination of the 1st Law and conservation of linear momentum to establish the necessity for a stationary gas CoM as a priliminary condition of thermodynamic equibrium in, for now, a defined NVE state. The next stage will be to recruit the conservation of angular momentum to establish that there can be no nett flow towards or away from the CoM at equilibrium ie that in the absence of input of external work or torque, the gas remains evenly distributed throughout the available volume. After that, well I trust that any residual ideas of macroscopic systems hopping willy-nilly between unrelated, random microstates will have dissipated. I thank you all in advance for forcing me to think through all this stuff carefully stage by stage. It's over 40 years since I sat through my last thermo lecture!

I specifically stated the centre of mass of the gas because this is precisely the quantity that you are trying to move around relative to the CoM of the box to establish your case.

If the centre of mass of the particles remains stationary at the centre of the box, then it's possible that no nett work has been performed on the gas. Now explain to me how that centre of mass can move towards the sides of the box to any reasonable degree without the box performing work on the gas.

Another interesting rabbit hole. By coincidence, I asked a question the other day about the strength of coupling between a CMB photon emitter and its TV aerial absorber. Mordred informed me that contrary to what I'd inferred from what I'd read of GR, they weren't actually touching since the photon wasn't a valid frame of reference. Obviously, I've no grounds whatsoever for disputing this, and too many Minecraft projects planned to try and get to grips with it. I just accept that for now and the foreseeable future, such fields are beyond my understanding. Not my system. You define your system as you wish. If you can. It's not easy, and perhaps will give some idea of why the microcanonical ensemble has given statistical mechanics some headaches in the past. The canonical and grand canonical ensembles find easier application in the real world and have no aberrant conflicts with classical thermodynamics. There is now an exchange of work between particles and box. It has become your very own 'undisclosed piston'. Do you now see and understand the issue?

An interesting rabbit hole! Firstly, consider what is happening to your system centre of mass, and account for its apparent irregular motion. I look forward to your well considered response (which I'll not preempt here)

My point. We're agreed. Agreed. The V/2 state perforce requires some combination of W and Q which must be reflected in a balancing change in U. 2nd Law implies a minimum increase in U (and hence T) under simple compression. They said it. Obviously. Absolute zero microstates are allowed into their ensemble by their reasoning. How do you propose to explain all the particles appearing in one half of the box? My inference is that there must be something equivalent to an undeclared piston compressing the system which, as you say, violates the conditions of the problem. That in itself is a clarification: the hypothesis is probably BS.

Your point that classical thermodynamics largely time independent, I accepted without seeing the need for further comment. Which was the other point? I'm 100% with Mordred on this issue. Would you be happy to simplify the thread and leave it at that? Then we are in agreement. Obviously. Hope all is clear

You do like to nit-pick! Depends a little on context. Formally, in my day job, it usually infers that the system is in a state of minimum Gibbs Free Energy - e.g there are no bulk convective processes going on within it. For a constant V, T system (I rarely encounter these) it would be a state of minimum Helmholtz Free Energy. In the OP scenario, the presenters start with an equilibrium V, T condition and claim that it can evolve spontaneously to occupy only V/2. This requires a bulk convective flow (eg a piston compressing it) and represents a fundamental change of state. The presenters concentrate on the position distribution of their system and fail to mention any impact on the momentum distribution. Do we infer the temperature has remained constant (breaking the 1st Law and the 2nd)? Has it increased as it would if it had been compressed by a piston (2nd Law preserved but not the 1st)? Or indeed has it decreased. We are left to guess. The only clue we have is that the presenters claim to have 'proven' evolution to a low entropy condition. If we believe them, this eliminates the higher temperature case from consideration. What we are left with is a proposed sudden and significant random change of state breaking both 1st and 2nd Laws. It's perhaps a personal flaw, but I've a habit of ridiculing such proposals by highlighting an extreme case that becomes allowable if their assumptions are correct. Such as a spontaneous jump to absolute zero. Of course the presenters do not state this inference explicitly as it would make them appear very foolish. But I'm quite happy to point out a logical extension of their false reasoning.

A hole as little as 1m below the water line of an atmospheric tank will produce a water jet around 4 m/s without being accelerated by anything other than the potential energy of its top surface, whereas suction lines for typical common-or-garden centrifugal pumps are rarely designed to run above 1 m/s, often much less. So the potential energy of the liquid top surface is more than sufficient to flood a pump suction without any assistance from the pump. The fact that some pump suctions are able to run at a partial vacuum is because the pump internals are sealed within an air-tight casing and cannot 'see' atmospheric pressure. The actual operating suction pressure is set by suction side static liquid head less friction losses and is independent of the pump. The pump simply adds its rated differential head to whatever absolute liquid head it's provided with at its suction flange, and that sets its discharge liquid head. As I said, there's no such force as suck.

I did. A box of volume V with all its contained particles sat in the left half is a non-equilibrium state, isn't it? As were each and everyone of the previous10^(big) intermediate microstates necessary to create this scenario. You're Wikipedia link introduced 'N .... a small number of particles'. I thought it might be useful to firm up the order of magnitude where this concept may have some significance. Something a bit smaller than say N = Avogadro's number. Similarly, you're link stated this small number of particles 'may show significant statistical deviations from that predicted by the second law' without quantifying it by example. So I provided an example. I wasn't changing the parameters. I was merely plugging in representative numbers where they had been left unquantified, woolly, and uninformative. Please read the quote this comment refers to: it paraphrased the Youtube presenters. For me, the relative temperatures of the two states were undefined therefore so were the relative entropies.

This. Rule 1) There is no such force as suck. All the energy for accelerating water out of the container comes from the container and its contents, so you can forget about everything downstream of the hole - it's irrelevant. In the vicinity of the hole the water converts some of its (undirected) internal energy into directed momentum heading left let's say. This results in a localised drop in internal pressure on the left hand side of the container while the right hand side of the container continues to see the higher local fluid pressure, and is hence kicked to the right by a nett reaction force equal and opposite to the momentum of the exiting water stream. In a small system, it's a small effect. Industrially, say when a large pressure relief valve opens - these reaction forces can be many tonnesf and require serious structural support.

Perhaps you didn't read my OP carefully - I dispute that these 'so-called second law violations' exist at all precisely because they ignore the concept of formal states. In particular these examples depict what I presume is a microcanonical ensemble (no heat bath is indicated) which in statistical mechanics (as I understand it at least) has a clearly defined equilibrium NVE state. ie the ensemble consists of all those possible accessible permutations of that number of particles (N) occupying a constant volume (V) within a vanishingly thin band of total energy (E). I trust that you agree that this corresponds to a formal state. The next slide presents (presumably) the same N particles occupying only half the volume, claiming that this an inescapable result of statistical mechanics. Would you agree that this corresponds to an entirely different formal state (with undefined total energy to boot)? Personally, I dispute that such a state could evolve for even the briefest of flickers because in that instant, it 'forgets' its earlier state - the information necessary for restoring it has been irretrievably lost due to the proposed macroscopic drop in entropy. The change would be permanent. This is significant. If we accept the smallest possibility of such an event, we accept higher frequency occurrence of less extreme random deviations and so on until we no longer have meaningful conservation laws - isolated systems would be continuously changing their properties in a continuous random walk with expected deviation propotional to the square root of time elapsed. I am amazed that so many seem to buy into this concept, without apparently the slightest shred of empirical evidence.

Many thanks, swansont. My reading of this passage draws two key inferences: 1) 'Each microstate that the system maybe in' refers specifically and only to the ensemble of microstates whose properties are consistent with those of the initial microstate and for which there is a credible mechanism through which each can be accessed (see ergodic hypothesis). It most definitely does not include any wacky extreme non-equilibrium microstate dreamt up by a Youtube presenter in search of more Patreon support. 2) A snapshot of a small number (like 42) particles doesn't have a precisely defined temperature etc due to the uncertainty principle and the relatively large error bars of a small dataset. However, this measurement problem is just that, isn't it? Hiding away inside the quantum fuzziness is there a possible state of 42 regularly spaced particles all with zero relative motion? I think not. There's no route in and out of such a state. I don't really follow quantum theory but I was under the impression that many of its leading lights were currently touting 'information cannot be destroyed' which pretty much underpins the 2nd Law, doesn't it? Actually there's a third now I think of it. The Wikipedia paragraph you referenced carries no inline references. I was rather hoping to find something on this subject that's been through a proper peer review.

In what way is the 2nd Law 'statistical'? Many notable researchers have used a statistical approach to probe the complexities of thermodynamic systems, but isn't that only because of the computational complexity? Are you claiming that the systems themselves are stochastic in a real sense? If so, then where does the random element creep in?

If fire can only be initiated by an earlier fire, how did the first fire start?