A major problem still pervading physics is the microscopic reversibilty condition.

On the macroscopic level, systems will evolve to configurations such that the entropy of this system is a maximum. This gives a definate direction to the ways things happen and evolve. Among the ramifications of this is the heat death of the universe as it tends to higher orders of entropy. The laws of equilibrium statistical mechanics holds here so long as we consider the universe to be a closed system, which may seem obvious, but in general we have no proof to say that it is.

On the microscopic level however, all processes seem to be symmetric in time in that there is no evidence suggesting that certain reactions or interactions are more or less probable if we "play" them in reverse.

One of the first clear cut divisions on this subject was when Boltzmann formulated his kinetic theory and consequently his H thereom, and shortly after when Poincare' gave us Poincare' cycles.

As far as I know this problem has not been resolved.

Is anybody here involved in such work or has relevant information as to the current situation of the problem, as it would greatly aid me.

Cheers:)

Originally posted by ryans


On the microscopic level however, all processes seem to be symmetric in time [...]
approximately

Hi ryans,

Interesting point (read: just the kind of thread I've been waiting for :)).

You mentioned Boltzmann's work and the corresponding H theorem. In the derivation of the Boltzmann equation, all steps are time-reversible, except for one ansatz he makes, the so called Stosszahlansatz or Molecular Chaos ansatz (in the Boltzmann context this assumption comes down to saying that after two particles collide, the outgoing velocity is randomly distributed - keeping conservation of momentum into account). This statistical ansatz introduces irreversibility in the Boltzmann equation.

I recommend reading the work of Mark Kac, more precisely the "Kac ring model", which is a very simple model to explain this Stosszahlansatz. From this model, one deduces that:
- The source of irreversibility is the fact that in our everyday lives, the objects we witness are macroscopic (number of particles of order 10^23).
- The time-scale at which we look is far less than the Poincare recurrence time, and hence, we never see those recurrences.

It is a very simple model, but there is a group of people that believes that these are indeed the sources of irreversibility for more complex systems aswel. A must-read is definitly Bricmont's <A HREF="http://arxiv.org/abs/chao-dyn/9603009">Science of chaos or chaos in science</A>, which also discusses the Kac ring model in Appendix A.

I already pointed out the work of Maes and Netocny regarding the relation between time reversibility and entropy production <A HREF="http://arxiv.org/abs/cond-mat/0202501">here</A>.

I would say that Kac's work solves the problem of irreversibility for the Boltzmann equation (aside from the Ring model, he also discusses a more general model in a book he wrote... I have it on my desk at work somewhere, but you can find the reference in Bricmont's article).

For quantum systems there is something like the Kac ring model aswel, but we're still working on a paper on that (should be finished by the end of the week, preprint should be on arxiv.org within 3-4 weeks). It turns out that also for a simple quantum model, there is relaxation to an equilibrium state if you look at large systems and at the proper timescale (i.e. experimentally accessible timescales like minutes, hours, years... but not at the lifetime of the universe where Poincare recurrences or quantum periodicity of finite systems could come into play).


Lethe,

The slight breaking of time-reversibility in nature could be related to minor increases of entropy (i.e. in a sense that always there is a small heat flow). As a matter of fact, any system involving (macroscopic) currents will break time reversibility (because these currents exactly give entropy production).


Bye!

Crisp

Originally posted by Crisp

Lethe,

The slight breaking of time-reversibility in nature could be related to minor increases of entropy (i.e. in a sense that always there is a small heat flow). As a matter of fact, any system involving (macroscopic) currents will break time reversibility (because these currents exactly give entropy production).


Bye!

Crisp

whoa. how is that possible? i mean, in a simple CP violating decay of one fundamental particle, are you saying that there is an increase in entropy? can you elaborate? i m having a hard time swallowing this.

Lethe and Crisp, can you give me one hard example of a microscopic process that does not posses time reversal symmetry, i.e. the reverse reaction is not possible, or has a far lower probability. By microscopic I am refering to the sub atomic regime.

Originally posted by ryans
Lethe and Crisp, can you give me one hard example of a microscopic process that does not posses time reversal symmetry, i.e. the reverse reaction is not possible, or has a far lower probability. By microscopic I am refering to the sub atomic regime.

kaon decay.

Good stuff, and this decay scheme shows definite increase in entropy. Correct me if I am wrong but I have a decay scheme here for Kaons taken from Kranes "Introductory nuclear physics" That for one initial state of a Kaon before decay, there is at least 6 decay schemes and thus an increase in the number of configurations. You can calculate the entropy of each system (before and after decay) using the statistical definition of entropy. I will do this shortly as I have probabilities for the decay configurations but not fot the long lived and short lived Kaon states.

Please correct me if I am wrong here. One major assumption I have made is that the 2 systems are in equalibrium. Is this valid?

Originally posted by ryans
Lethe and Crisp, can you give me one hard example of a microscopic process that does not posses time reversal symmetry, i.e. the reverse reaction is not possible, or has a far lower probability. By microscopic I am refering to the sub atomic regime.

uhh... lemme explain a little further.

there isn t really a way to measure T violation, because we don t know how to make time run backwards. but it is known that CPT must be an exact symmetry, not only in the standard model, but in every extension to the standard model. there are various reasons to believe that CPT must be exact in any theory.

and it is clear that if CPT is an exact symmetry, then if T is violated, CP is violated, and conversely, if CP is violated, then T must be violated. so to see for T violation, we look for CP violation.

now CP violation is what is measured in kaon decay. it is not, as you say "far lower probability". the branching ratio is something like 49.9% and 50.1%. it s pretty weak violation,but it is definitely within the bounds of experimental verification. and that is why i said "approximately" before. T very nearly, but not exactly an exact symmetry. unlike P which is maximally violated by the weak force.

Originally posted by ryans
Good stuff, and this decay scheme shows definite increase in entropy. Correct me if I am wrong but I have a decay scheme here for Kaons taken from Kranes "Introductory nuclear physics" That for one initial state of a Kaon before decay, there is at least 6 decay schemes and thus an increase in the number of configurations. You can calculate the entropy of each system (before and after decay) using the statistical definition of entropy. I will do this shortly as I have probabilities for the decay configurations but not fot the long lived and short lived Kaon states.

Please correct me if I am wrong here. One major assumption I have made is that the 2 systems are in equalibrium. Is this valid?

i guess entropy does increase for this reaction, since it decays into multiple particles. however, i believe that the findamental reaction going on is a simple reaction of the quarks, and in some high energy reaction, with asymptotically free quarks, we would still see this symmetry violation, even with single particle reactions.

and what do you mean by equilibrium? what does that mean for a single particle, like the kaon?

Yes but it is this microscopic assymetry which is required so that they may be manifest on a larger scale as entropy production and the tendancy or infallible prediction that systems will drive towards configurations that posses higher entropy. So it is this symmetry breaking that is required.

Originally posted by ryans
Yes but it is this microscopic assymetry which is required so that they may be manifest on a larger scale as entropy production and the tendancy or infallible prediction that systems will drive towards configurations that posses higher entropy. So it is this symmetry breaking that is required.

well, i m not quite following you. are you saying that this T violation is the source of the arrow of time in the macroscopic second law of thermodynamics?

the whole thing is a little confusing to me, and i m definitely not very comfortable with talking about the entropy change in a fundamental particle reaction, but i am interested to hear what you and others think about this.

The whole thing is that on the macroscopic scale, thermodynamic processes give a definate arrow to the direction of time. Eggs don't spontaneously reassemble from the fragments of a broken shell, white and yolk. The universe is driving itself to higher orders of entropy on the macroscopic scale.
On the microscopic scale however, time seems to have no arrow. The processes that break up the egg, chemical reactions and the like, are just as probable in one direction as the other.
For example take alpha decay. I am sure you know this so I won't say it to you like you are an idiot. An approximate model here is the preformation of the alpha particle in the nucleus and the subsequent tunnelling through the potential of the nucleus, correct? In the other direction, an alpha particle which has sufficiently lower energy than the height of this potential is able to tunnel through this barrier INTO the nucleus. Each case seems to have a corresponding increase in entropy as given an alpha and nucleus in some initial state, the number of final states far out ways the number of initial states (i.e. decays leaving the nuclues in an excited state, then the subsequent emission od a photon). I have no doubt that your knowledge of nuclear processes is far superior to mine Lethe, as this is your field, but the time reversibility of these reactions seems to be in contradiction with the second law of thermodyanamics. I am sure this issue has already been resolved, but the question that remains is

How to macroscopic processes which seem to be temporaly uni-directional arise from microscopic processes which are symmetric w.r.t. time reversal?

Hi lethe,

I agree that I also feel a bit uncomfortable talking about the entropy about one particle... There are probably some ways to get around this (to measure the 49.1% / 50.1% ratios you need to do loads of measurements involving loads of particles blablablabla), but it remains tricky...

However, I was just speculating on the breaking of time reversibility on that scale. The cause is probably more fundamental than the breaking of reversibility at a macroscopic scale.



Ryans,

"How to macroscopic processes which seem to be temporaly uni-directional arise from microscopic processes which are symmetric w.r.t. time reversal?"

Okay, you've asked for it, now you're going to get the hardcore math ;)...

1. There is increase in entropy

First of all, let's assume that we have an autonomous and deterministic equation on a macroscopic scale (e.g. a solution of the Boltzmann equation, Navier-Stokes equation, Euler equation, ... pick one). Since this equation is autonomous, there are no extra parameters needed to find the state of the system at time t from the state at time 0. Since this equation is determininistic, if I start the system in a state M(0) and I evolve to state M(t), then everytime I start the system in M(0) I will get back M(t) again.

The trick is now to realize that the states I am talking about are macroscopic states. So, what is a macroscopic state ? Simple: a partitioning of phasespace into fewer parts (coarse graining of phase space). And by Boltzmann, the entropy of such a macroscopic state is simply the logarithm the Liouville phasespace volume |M(0)|.

Now the Jaynes argument for the increase of entropy: start the system in a macrostate M(0) . At time t, every microstate from M(0) will have evolved to a microstate which belongs to macrostate M(t). That must be so because we assumed a deterministic & autonomous macroscopic equation. So we surely have

microstate in M(0) at time 0 --> microstate in M(t) at time t

Because M(t) can even contain MORE macrostates, we therefor must have |M(0)| =< |M(t)| ... Or taking the logarithm, we find that the entropy must increase.

This beautifully simply argument states that if you can find an autonomous and deterministic equation on a macroscopic scale, then you must have something like an H-theorem and thus breaking of time reversibility!


2. How do you get autonomous, deterministic equations

This is the tricky part. Given a (time reversible) microscopic dynamics, how can you construct an autonomous and deterministic equation on a macroscale ? Let's say that the macroscopic, deterministic & autonomous equation describing how the observable A evolves in time is written as a(t) ... if it exists.

First of all, we're talking about macroscopic effects (breaking of time reversibility... we're not talking about the kaon thingy here, only about Newton's equation, Schrodinger equation... etc... which are microscopically reversible). So we're going to work with an ensemble E of some kind. We have of the order of 10^23 particles in our system, so we're going to use statistics (think of the canonical or microcanonical ensemble in equilibrium statistical mechanics... this won't work here since we're dealing with time evolutions, but assume there is some kind of statistical ensemble E that does work outside equilibrium). This means that the time-evolution of our observable A .. lets write the microscopically time-evolved as A(t) ... will be expressed as some kind of statistical average over our ensemble E. So what we are doing is: we apply the microscopic dynamics to the system, and then calculate the expectation value of the observable A(t) ...

This A(t) has some kind of probability distribution (because of the underlying ensemble statistics). What we want to prove is that when you have a large number of systems, this probability distribution converges to a dirac measure on the deterministic and autonomous equation a(t).... i.e. the ensemble-average of A(t) converges to a(t) and the variance converges to zero.

This would be good, because that would mean that typically, you would see the a(t) behaviour in your system. And if you see the deterministic and autonomous a(t) behaviour, then there must be an increase of entropy.


So to conclude: suppose you have an ensemble which gives rise to an autonomous macroscopic equation (which in fact *should* be the case, all macroscopic equations like Navier-Stokes or Boltzmann are deterministic and autonomous and they are accurate on that macroscopic scale)... So you have this macroscopic equation, then you must eventually wind up with a breaking of time reversibility.


Hope this is somewhat clear, feel free to ask questions :)

Bye!

Crisp

This means that the time-evolution of our observable A .. lets write the microscopically time-evolved as A(t) ... will be expressed as some kind of statistical average over our ensemble E. So what we are doing is: we apply the microscopic dynamics to the system, and then calculate the expectation value of the observable A(t) ...

Aren't you describing here some autocorrelation function such as the velocity correlation function for a Brownian particle following the Langevin equation?

There are a whole heap of correlation functions, but that still does not address the issue for time reversibility. Take a time correlation function. It is symmetric w.r.t. inversion of phase space, and time reversal, and is arbitary of the time origin chosen. And so there is no prefered direction for a systen to evolve in.

Hi ryans,

Aren't you describing here some autocorrelation function such as the velocity correlation function for a Brownian particle following the Langevin equation?

Ehrrr... no, just the expectation value of a general observable (not necessarily for correlations). The point is that there are two ways to calculate the evolution of the system: either you look at one specific microscopic realisation of an evolution of your system, which is A(t) and for all practical purposes too hard to calculate (you want to solve an equation with 10^23 variables?) or you look at it from a statistical approach, where you attach a certain weight to every possible microscopic realisation (= defining an ensemble) and then look at the average behaviour in the ensemble.

You should really think of that weight as a "generalised" Gibbs measure exp(-beta H), but then out of equilibrium.

BTW: I am deliberately being vague here, simply because I don't know the answer (I think no-one does because that would kinda solve the whole non-equilibrium statistical mechanics problem). I was just sketching how the ensemble approach would inevitably lead to an H-theorem.

Bye!

Crisp

I am deliberately being vague here, simply because I don't know the answer (I think no-one does because that would kinda solve the whole non-equilibrium statistical mechanics problem). I was just sketching how the ensemble approach would inevitably lead to an H-theorem.

That is true, no-one really knows the answer. I am hoping to get some money next year to investigate this stuff, but for now it's only in my spare time. Keep going though, it's helping.

Originally posted by ryans


One of the first clear cut divisions on this subject was when Boltzmann formulated his kinetic theory and consequently his H thereom, and shortly after when Poincare' gave us Poincare' cycles.


ryans (or anyone), i have no idea what this H-theorem is, or what it has to do time reversal symmetry. would you mind explaining this theorem for me?

In short, Boltzmann defined a quantity H, which is a function of the velocity distribution of the particles in the system. For a gas that is in a state of molecular chaos (this definition in itself is a bit tricky), then the time derivative of H is always less than or equal to 0. This gives a direction for which a system will evolve. It would be nice to show you the math, so I will try and make some time to construct an attachment.

The assumption of molecular chaos is a bit of a misnomer in that its name betrays its form.

You know about distribution functions right. It simply says that the pair distribution function is the product of 2 representative single particle distribution functions. There is an analogy in quantum mechanics which is the Hartree product. You know that the many-body wavefunction is the product of single particle wavefunctions. I know that this is wrong in QM, but it seems to be valid here.

I will work on that attachment.:)

Hi lethe,

I just would like some historical comment to Ryans' explanation: Boltzmann believed that the proof of his H theorem formed a mechanical explanation of the second law of thermodynamics (mechanical in the sense that he was able to derive that the H function always decreases in time for a dilute gas that only interacts through Newtonian collisions). He argued that minus the H-function (which always increases) could be interpreted as the monoticity of the entropy.

Nowadays people are a bit more careful to call it an entropy, but nevertheless, the indication that there exists a function that always increases/decreases clearly singles out a prefered direction in time, i.e. it breaks the time reversibility of the underlying Newtonian dynamics.

Bye!

Crisp

Nowadays people are a bit more careful to call it an entropy, but nevertheless, the indication that there exists a function that always increases/decreases clearly singles out a prefered direction in time, i.e. it breaks the time reversibility of the underlying Newtonian dynamics.

Crisp,

I agree with you entirely but I think the problem here is that even if a function is obtained to describe macroscopic behaviour, we still have the undeniable reality that on the microscopic level, all processes seem to be reversible. It has more to do with the cooperated movement of the constituents of the system, and why they seems to "cooperate" to minimise say the free energy of the system, on a microscopic scale, than to find a macroscopic function which simply side steps the issue.

Hi ryans,

I agree, but I was trying to offer an explanation on why this happens... I think it is a fundamental consequence of the fact that you use statistics, and this physically is ofcourse because you have a large number of constituents.

Also note that minimisation of free energy, increase of entropy or whatever are macroscopic concepts, F = U - TS (i.e. in the microscopic world they are not defined), so you have to take care in saying that microscopically "free energy is minimised"... I think it is better to say that you have to understand why free energy is minimised on a macroscopic scale, and this question is imho equivalent to saying why entropy increases. And this leads me back to what I think is the answer: statistics ;)

Bye!

Crisp

I'm not clear on the problem. I don't see any conflict between microscopic reversibility and macroscopic irreversibility, but maybe I'm missing the point of your post.

For example, take a deck consisting of 2 cards. Shuffle it until the order changes. Then do it again. You get the original order back -- reversibility! Now do it with a 52 card deck. You can keep shuffling until doomsday, but you'll never get the original order back -- irreversibility.

Originally posted by StrangeDays
Now do it with a 52 card deck. You can keep shuffling until doomsday, but you'll never get the original order back -- irreversibility.

never :bugeye: ? are you sure?

never ? are you sure?
If you believe in an eternal afterlife that includes playing cards, then maybe you have a chance.

There is a definate probablity that in a deck of cards that you will get the original order back. There are in fact 52! possible configurations of the cards, with each configuration being of equal probability. This is very analogous to Poincare' cycles in that if wqe wait long enough any configuration is possible.

Originally posted by StrangeDays
For example, take a deck consisting of 2 cards. Shuffle it until the order changes. Then do it again. You get the original order back -- reversibility! Now do it with a 52 card deck. You can keep shuffling until doomsday, but you'll never get the original order back -- irreversibility.

What you're talking is recurrence of the original order. There is a probability. But Reversibility is tracing back to the orginal order. That is difficult in a random process like this.

And a cup of coffee that has cooled to room temperature has a nonzero probability of spontaneously boiling again, but we still consider the cooling process to be irreversible. The 2nd law of thermo assumes that significant spontaneous decreases in entropy are improbable enough to sweep under the rug, which is a good assumption even in systems as simple as a 52 card deck.

AHAH,

But the cup of coffee is an open system, the deck of cards is not. And your example is exactly what we are talking about.

Put the cup of coffee in a container that is totally isolated from the rest of the universe (this is a thought experiment, the second law of thermodynamics is also an ideal case which has non-achievable states as there are really no reversible processes)

The cup of coffee and the "atmosphere" inside the box will reach equilibrium whereby there temperatures are the same. Poincare' proposed (or proved) that there is a finite but really small probabilty that yes the cup of coffee at some stage will heat up.

The deck of cards has constant entropy, as entropy is a function of the entire ensemble of configurations, not one configuration. It is therefore non-sensicle to talk about the entropy of a particular configuration, as all configurations are equally probable. You are confusing objective disorder with subjective disorder.

The ordered set of numbers {2,4,1,5,3} is no more or less random than {1,2,3,4,5}, as both have equal probabilities of occurance out of a set of integers from 1->5 where each number can appear only once.

So the original configuration of a deck of cards that is ordered by suite and strength is no more probable than any other configuration, as all cards are distinguishable, just like the integers.

Hi ryans,

But even for closed systems you can have the same problem of macroscopic irreversibility... You just have to look at the proper timescale, and this is indeed what Strangedays was talking about: if you have a microscopic Hamiltonian evolution then you simply know that at some point the system will Poincare recur, but the time required is tremendously large. So the explanation for "increase in entropy" refers to locality in time: on "small" timescales, those accessible to the experiment, we see irreversible behaviour, but looking at the big picture, you find back the periodicity and reversibility...

This is why I emphasized that you should look at macroscopic systems (large Poincare times; but also because these are the systems we work with in our everyday lives), and at the proper timescales (otherwise you wont see irreversible behaviour).

The thing that one would like to understand even for simple closed systems is why the system appears to behave irreversible at our everyday timescales. Perhaps after we've understood that (and I think there are some models out there that tackle this question correctly), then we can have a look at open systems.

Bye!

Crisp

Ryans is right; my card analogy was poorly stated. In order to meaningfully discuss the entropy of any system, you have to define your macroscopic states, after which you can determine each state's entropy by counting the number of microscopic states that comprise it.

If we define a certain card ordering as a macro state and all other orderings as another macro state, then the entropy difference between our two states is enormous. The system will go to the state of high entropy and stay there for a very long time. But if we define each card ordering as its own macro state, then the entropy of our system never changes, which isn't very interesting.

The coffee example is analogous to the first way of defining macro states, with equilibrium being the high entropy state. Thermo tells us that it will stay in equilibrium forever, but that's a dirty lie propagated by lazy scientists who don't want to take a statistical approach when gazillions of micro states are involved.:)

As far as the original issue of microscopic vs. macroscopic, it's all statistics. If you take a box with a hundred coins, all heads, and shake it, you'll probably never get back to the all heads state. But the individual coins have no problem going back to the heads state. Microscopic reversibility and macroscopic irreversibility.

Hi StrangeDays,

If we define a certain card ordering as a macro state and all other orderings as another macro state, then the entropy difference between our two states is enormous. The system will go to the state of high entropy and stay there for a very long time. But if we define each card ordering as its own macro state, then the entropy of our system never changes, which isn't very interesting.

Very well said, that is exactly why you need to introduce coarse-graining in order to be able to talk of entropy: you are forced to divide your phasespace into grains (according to your choice of macroscopic observables) and then you can talk about entropy (eg as being the Liouville volume of the grain your system is in). If you choose every microstate as a grain (corresponding to choosing every card ordening as its own macrostate) then you are dealing with a microscopic system, for which entropy is ill-defined (in this case it would always be zero).

"As far as the original issue of microscopic vs. macroscopic, it's all statistics. If you take a box with a hundred coins, all heads, and shake it, you'll probably never get back to the all heads state. But the individual coins have no problem going back to the heads state. Microscopic reversibility and macroscopic irreversibility."

This is exactly the Jaynes argument I (tried to) explain above, and also the most common interpretation for the increase of Boltzmann entropy: typically equilibrium corresponds to an overwhelming amount of microstates (compared to the non-equilibrium states) so your system, purely statistically speaking, is most lickely to be found in equilibrium after a while. This intuitive reasoning can be made more formal using autonomous equations, and then you get the Jaynes argument I was talking about.

The card ordening example you mentioned is not really ill-defined, you forget to mention what you take as macrostates. Aside from that, it is a perfect example of a closed system.

Bye!

Crisp

Sorry to bother y'all, but I am just wondering. If a Poincare cycle is just a fancy way of saying that you will eventually wind up back where you started by shear luck, then does this really just imply a cyclic nature rather than a reversible one. In other words, there is a difference between positive and negative frequency. Or, the tires on your car follow a cycle, but it still has a definite direction, otherwise you would go backwards (the whole car, I mean).

Do I have the Poincare thing all wrong?

Hi errandir,

If a Poincare cycle is just a fancy way of saying that you will eventually wind up back where you started by shear luck, then does this really just imply a cyclic nature rather than a reversible one. In other words, there is a difference between positive and negative frequency. Or, the tires on your car follow a cycle, but it still has a definite direction, otherwise you would go backwards (the whole car, I mean).

Well, you do not end up exactly where you started, but very very close to how you started (lets say that one atom or one electron could be in a different position). Also, it is not by shear luck, but really by physical laws.

But you are right, it implies cyclicity in nature, and it is a perfectly good question to ask why it comes up in a discussion about irreversibility then. Perhaps an example could illustrate this.

Right now I am drinking a nice hot cup of coffee. If I wouldn't drink it but instead leave it standing for an hour, the coffee would cool down to room temperature. However, the cup of coffee would not spontaneously take back some heat from the room and warm up again. This will not happen if I wait for another hour, or a day, week, century or 100.000 years. Nobody has ever witnessed cups of coffee heating up again spontaneously. Hence we say that the cooling down of the coffee is an irreversible proces.

But that is not entirely correct. The laws of physics (the Poincare recurrence theorem) predicts that it will heat up again one day (but it will take very, very, very long, like 10^10^23 seconds, that is a 1 with 10^23 zeros after it, dont start writing that number down ;)). It will not be 100% exactly the same cup of coffee (i.e. it will not heat up exactly to the 50°C it is now, but rather to 49.9999 °C), but leaving that miniscule difference aside, we can say that it will heat up again.

But there is a small problem ofcourse, and that is that it takes many many times the age of the universe before this happens. Therefor we can safely say that in our universe, nobody will ever see cups of coffee heating up again. It is a matter of looking at the right time intervals: for our daily experience (where time intervals like seconds, days, years or even centuries are important), no such thing as spontaneous reheating occurs. For our daily experience, time irreversibility is a fact.

You could say that time irreversibility then fundamentally does not exist, since this Poincare recurrence does seem to occur. Well, that is not the whole story, because on a more probabilistic scale, we can say that the probability that a cup of coffee, governed by e.g. Newton's equation of motion, cools down is 100%. We know it will cool down. However, according to the Newton's equation, if you stir your cold coffee just right, the probability to heat it up again by the right stir is also 100% (i.e. by properly shaking it you should be able to heat it up again). This clearly does not happen, so there is more to irreversibility than just "something that happens because we don't live long enough to see the Poincare recurrence".

Hope this explains it a bit,

Bye!

Crisp

It almost helps. I have thought of a better example. The gear in a clock (what an ironic example) that looks like a saw blade. There is some spring loaded mechanism (I don't know the name) that gets dragged across the incline of a tooth. At the top of the inlcine, the mechanism snaps back down to the bottom of the next incline. In a naive way, I am thinking of the position of the mechanism and the gear like a kind of state. The gear is not allowed to spin backwards by design, but it will eventually be back where it started. If I'm understanding the coffe example, it is similar? The coffee "snaps" back very rapidly to 50 C? If it gradually warmed to 50 C as gradually as it cooled over eons, then I'm not understanding this quite yet. It seems that, if this gradual interpretation were valid, we would be observing it by now in something.

Hi errandir,

The clock example is not really applicable I think. Let me first explain something you said:

If I'm understanding the coffe example, it is similar? The coffee "snaps" back very rapidly to 50 C? If it gradually warmed to 50 C as gradually as it cooled over eons, then I'm not understanding this quite yet. It seems that, if this gradual interpretation were valid, we would be observing it by now in something.

No, the coffee gradually warms up again. But you have to realise that this only takes an hour or so. The cooling of the coffee takes one hour (then it has reached room temperature), and it will stay at room temperature "for eons" until it heats back up in an hour.

I am not sure if the heating up time would be the same actually, I think it depends quite heavily on the kind of microscopic dynamics involved... I doubt it would be exactly the same as the cooling time, but it will surely be the same order of magnitude (i.e. the cooling can take 2 hours or a day even, compared to the 10^10^23 seconds you have to wait this is nothing ;)).

Bye!

Crisp

There are an infinite number of ways and times the cup of coffee could heat up again. The process is not important, because entropic arguements are not valid here. All that matters is the final confinguration, and there are as good as an infinite number of configurations which would have the cup of coffee at a higher temperature again.

Thanks, guys. I guess I will read about this Poincare in a lot more depth.

An interesting bit of reading for you all...

http://www.cheniere.org/articles/2ndLaw.htm

Yeah yeah I know, just read it anyway :eek:

Hi Blaah!,

I am absolutely stunned by the amount of misconceptions one can read in every paragraph of that text. I don't even know where to start tearing apart this text, the first line is already dubious :)... What the heck is "negentropy".. oh my god... crap overload... crap overload :D.

Bye!

Crisp

No equations

Therefore

No rigorous proof

Therefore

Not science

He has some interesting arguements, but in science we do not write essays on the way we think the world works. We derive proofs, perform experiements and state results. The interpretation is left to the entire scientific community.
There are no proofs, and no statement of results, such this is philosophy, not physics.

Definately more philosophy than physics, but I think it is only a magazine article not a thesis. I'm assuming "negentropy" is his term for reverse entropy reactions. Ya gotta give the guy points for open-mindedness. :)

I'll give you a hint on magazine articles

New scientist is to science as Dolly or Cleo is to world politics