What causes the arrow of time ?

[Careful]

That model is exactly IRREVERSIBLE. You are not solving reversible equations of motion. There are, implicit, irreversible points in the model. Those irreversible points appears when you study the system with great care and mathematical detail. In fact, remember that initially Boltzmann claimed that had derived the Second law of thermodynamics from reversible Newton equation. After -with more rigorous treatments- it was proven that it was really using an irreversible model.
.

That is a bold claim ! You do not even have control over the mechanisms and the relevant variables which make the separation between both chambers dissapear. Where is this so called proof whose existence you seem to claim ??

Moreover, can you define this collision operator for me (I guess it is just a heuristic object which attaches to an initial beam of particles colliding a final beam of particles?). Basically, what you seem to say is that any Newtonian mechanism which can explain this operator needs odd velocity dependent terms in the force. What is the PHYSICAL principle, determination procedure, behind this operator?

 

[vanesch]

What is reversible is, and only is, the motion of particle before and after each collision. But the overall motion (i.e. with collisions) is not reversible
For your model you would use
| <--O
with | the wall, but is the same. Since you would use an irreversible collision operator wall-balls.

The collision of an elastic ball with a rigid wall is not reversible ??

 

[Juan R.]

Moreover, can you define this collision operator for me (I guess it is just a heuristic object which attaches to an initial beam of particles colliding a final beam of particles?). Basically, what you seem to say is that any Newtonian mechanism which can explain this operator needs odd velocity dependent terms in the force. What is the PHYSICAL principle, determination procedure, behind this operator?

It is all available in a thing called literature: books, monographs, papers in journals, etc, etc, etc.

Probably Prigogine popular book was a goog begin for begginers as you. When you find a kind as ^{1 2}, etc. That are references... Look at the final of the book... search the text near the number that you are interested on... Next ask in the library for that book, monograph, article, etc... after read it...

 

[Juan R.]

The collision of an elastic ball with a rigid wall is not reversible ??

That would be of science without people as smart as you!

Well, since my repeated advice that you would read at least basic textbooks before reply irrlevant stuff has not worked...

 

[Careful]

It is all available in a thing called literature: books, monographs, papers in journals, etc, etc, etc.
Probably Prigogine popular book was a goog begin for begginers as you. When you find a kind as ^{1 2}, etc. That are references... Look at the final of the book... search the text near the number that you are interested on... Next ask in the library for that book, monograph, article, etc... after read it...

Now, you do not have to start being insultive for no reason at all. I want a PRECISE reference for this NO GO theorem (I hope you can give me one) - and I remember even partially supporting your position. Moreover, I am sure it does not take more than 3 lines to give me this definition and I hope you are intelligent enough to make it clear to anyone here. And stop referring Van Kampen, he is the kind of person who wipes away serious problems in HIS reasoning by bold, handwaving claims which is amusing (as Bell makes fun of him in his book), but not very instructive.

 

[Hans de Vries]

to vanesch:
prove -at least by one time- to read literature in a topic before claim your own irrelevant and totally wrong ideas.

I dunno, So much utter nonsense has been produced in the literature on this subject!
Why waste time with all those other people's "irrelevant and totally wrong ideas"?

Irreversibility is right under our nose:

Irreversible physics:
-gravity
-strong force
-weak force
-electro magnetic force

Reversible physics:
-heat/kinetic energy
-Pauli's exclusion principle

Almost everything is irreversible:

Gravity has to be repulsive in order to organize matter into stars and
galaxies backward in time. Equal charges have attract to and opposite
charges have to repel for EM to work backwards in time.

There's no point on basing an entire discussion on one of the very few
physical processes that is symmetric in time with a quantity called entropy
which completely fails to describe what we want.Regards, Hans

 

[vanesch]

That would be of science without people as smart as you!
Well, since my repeated advice that you would read at least basic textbooks before reply irrlevant stuff has not worked...

Juan, your "arguments" seem to be based only on reference to authority and denigration of other posters. This is not an attitude that will prove very productive. I don't learn much from your replies. Now, that could be my problem or yours, but given the fact that I learn from other's replies, there is at least indirect evidence that the problem lies with you.

You are entitled to jokes. Not to insults.

 

[vanesch]

Gravity has to be repulsive in order to organize matter into stars and
galaxies backward in time. Equal charges have to repel and opposite
charges have to attract for EM to work backwards in time.

?

That's not true! Replace t by -t in Newton's equation with Newtonian gravity, and you won't see the difference ! Do the same with Maxwell.

BTW, equal charges DO repel (forward or backwards in time), and if you have several masses interacting gravitationally, and you REVERSE all momenta, then you follow the motion exactly with time running backwards (in Newtonian gravity).

The gravitational lumping only occurs because there are OTHER processes (mainly radiation) who take away energy of the gravitational system (still in Newtonian gravity). Otherwise, a random cloud of particles interacting gravitationally would not noticably shrink over time. But because the kinetic energy of the particles is converted into (heat) radiation for instance, gravity can succeed in shrinking a gas cloud. But not on its own.

 

[Hans de Vries]

Entropy is incapable of distinguising between exteme opposites.

-
-
In an arrow of time discussion one wants to discuss the evolution from
randomness and chaos to highly evolved, complex organized systems.

Entropy gives both extreme opposites a higher value. So it can not even
properly distinguish between the begin and end situation.


More complex, higher evolved, organized systems -----> higher entropy.
More chaotic, random, unorganized systems ----> higher entropy.


Regards, Hans.

 

[Careful]

-
-
In an arrow of time discussion one wants to discuss the evolution from
randomness and chaos to highly evolved, complex organized systems.
Entropy gives both extreme opposites a higher value. So it can not even
properly distinguish between the begin and end situation.
More complex, higher evolved, organized systems -----> higher entropy.
More chaotic, random, unorganized systems ----> higher entropy.
Regards, Hans.

Now you don't even have to bother anymore about giving a precise definition of entropy since in your statement entropy, whatever it is, increases by logic An inconsistent logic, I must add, unless entropy stays constant all the time.

 

[Hans de Vries]

?
That's not true! Replace t by -t in Newton's equation with Newtonian gravity, and you won't see the difference ! Do the same with Maxwell.

Take as a start situation two stationary masses or two stationary charges.
You have to reverse the forces to get equal behavior backward in time.
It does not work if you reverse the (zero) momentum here.

In ideal systems the potential energy is 100% converted to kinetic energy
giving an illusion of reversibility as long as kinetic energy is preserved
perfectly.

The momentum is not a part of the forces mentioned therefore I wouldn't
say that the forces themselves are reversible.


Regards, Hans

 

[Hans de Vries]

Now you don't even have to bother anymore about giving a precise definition of entropy since in your statement entropy, whatever it is, increases by logic

Complete uniformity has the lowest entropy.

Take a silicon surface with a highly regular grid. (very low entropy)

You can increase the entropy in two ways:

1) Prepare the surface for a highly complex micro processor ----> higher entropy.

2) Melt the surface -----> higher entropy.

You see, Entropy as is doesn't describe what you want if you want to
measure the process of evolution from randomness and chaos to highly
complex organized systems.


Regards, Hans

 

[vanesch]

Take as a start situation two stationary masses or two stationary charges.
You have to reverse the forces to get equal behavior backward in time.

Ok, look at two stationary masses 1 a.u. away from each other at t = 0, and apply Newtonian gravity. Consider this a boundary condition and solve the differential equation for motion for all t (negative as well as positive).
Now flip the graph so that t -> -t. Do you see any difference ?

Simpler example: consider an apple 5 meters above the ground, velocity 0. Solve the equation of motion for all t. Flip t -> -t. Any difference ?

 

[Hans de Vries]

Ok, look at two stationary masses 1 a.u. away from each other at t = 0, and apply Newtonian gravity. Consider this a boundary condition and solve the differential equation for motion for all t (negative as well as positive).
Now flip the graph so that t -> -t. Do you see any difference ?
Simpler example: consider an apple 5 meters above the ground, velocity 0. Solve the equation of motion for all t. Flip t -> -t. Any difference ?

Off course, because your equation of motion includes both the force and
the stored kinetic energy (and not the air resistance for example)
It's only the combination of the two which gives an illusion of reversibility.

Accelerated charges will radiate energy away for instance. Not all potential
energy is converted to kinetic energy.

Regards, Hans.

 

[vanesch]

Off course, because your equation of motion includes both the force and
the stored kinetic energy (and not the air resistance for example)

We started off with an empty universe with two masses, right ?

 

[Hans de Vries]

We started off with an empty universe with two masses, right ?

Wasn't is a single one? I guess that's when all the trouble started

 

[vanesch]

Wasn't is a single one? I guess that's when all the trouble started

"In the beginning, the universe was created ; and many people considered that a bad move"

No, I meant: a Newtonian universe with 2 masses. That's what you gave as an example of an irreversible (?) process in

Take as a start situation two stationary masses or two stationary charges.
You have to reverse the forces to get equal behavior backward in time.
It does not work if you reverse the (zero) momentum here.

 

[Juan R.]

I want a PRECISE reference for this NO GO theorem (I hope you can give me one) - and I remember even partially supporting your position. Moreover, I am sure it does not take more than 3 lines to give me this definition and I hope you are intelligent enough to make it clear to anyone here. And stop referring Van Kampen, he is the kind of person who wipes away serious problems in HIS reasoning by bold, handwaving claims which is amusing (as Bell makes fun of him in his book), but not very instructive.

I already cited for you...

Read above...

Read the book...

Read all but specially chapters 3 and 5...

Look the ^{1 2 3}

Etc.

 

[Careful]

I already cited for you...
Read above...
Read the book...
Read all but specially chapters 3 and 5...
Look the ^{1 2 3}
Etc.

Ok, I will go and look up the Prigogine book provided you can *clearly* answer me the following question :

In the example of the box with two chambers, how can you *prove* that taking away the wall and the consequent irreversible behavior of the gas *cannot* be described by reversible physics combined with suitable intial conditions on time scales smaller than the recurrence time. It is sufficient to give the main plausible arguments which make this clear. I am sure that an enlightening discussion of this particular example shall win many people for the point you try to advocate.

Cheers,

Careful

 

[Careful]

It is really interesting -from my personal point of view- that smart people is researching if Weyl hyphotesis (that is, asymmetry on R_{ab} due to singularity theorems) is the basis of irreversibility...
or if it is the asymetric character of target space in noncritical string theory (what is a generalization of standard string theory which is time symmetric)...
or if it is that at the big bang, Universe suffered a phase transition from vacuum, and we are living in an universe with Brushels Scool semigroup ..

The Weyl = 0 curvature hypothesis is a classical assumption on the initial phase of the universe in a *time reversal invariant* theory (classical GR, so very special intial conditions). This is exactly why this should NOT make you happy ! However, as said before, it is not crystal clear how the horizon area of black holes relates to fundamental degrees of freedom of spacetime (and as such to ``entropy´´ although the similarity is striking). But for sure, the horizon area of black holes gives a deterministic arrow of time.

Cheers,

Careful

 

[Juan R.]

Ok, I will go and look up the Prigogine book provided you can *clearly* answer me the following question :
In the example of the box with two chambers, how can you *prove* that taking away the wall and the consequent irreversible behavior of the gas *cannot* be described by reversible physics combined with suitable intial conditions on time scales smaller than the recurrence time. It is sufficient to give the main plausible arguments which make this clear. I am sure that an enlightening discussion of this particular example shall win many people for the point you try to advocate.
Cheers,
Careful

Because from initial conditions more reversible physics one does not obtain irreversible equations. This is the reason that nobody can explain the behavior of a dense fluid using reversible dynamics more initial conditions alone. If irreversible phenomena was explained via initial conditions and Newton or Schrödinger equations then would not exist a field of science called non-equilibrium statistical physics, where people want obtain just irreversible equations as those of Boltzmann.

 

[Juan R.]

I find very very interesting, that during more than 125 years some of the most brilliant physicists and chemists of history, lot of them true recognized and very well versed specialists on statistical physics, nonlinear chemistry, quantum theory, etc. and at least 12 Nobel Prizes and other great guys as Penrose, Hawking, etc. have worked in the topic.

From the simplistic 19th century models of elastic balls, people now is studying models of quantum gravity, spacetime decoherence via Ito integrals, RHS (Gelfand triplets) approaches, etc.

It is really interesting -from my personal point of view- that smart people is researching if Weyl hyphotesis (that is, asymmetry on R_{ab} due to singularity theorems) is the basis of irreversibility...

or if it is the asymetric character of target space in noncritical string theory (what is a generalization of standard string theory which is time symmetric)...

or if it is that at the big bang, Universe suffered a phase transition from vacuum, and we are living in an universe with Brushels Scool semigroup \Gamma^{+}...

but nothing of that is needed because acording to some physicists as Lebowitz and others, the basis of irreversibility is easily proven via a model of classical balls in a box. The problem is that those dozens and dozens of smart people was unable to understand as a model of all balls in a half part of the box 'explains' irreversibility.

I just find those interesting, very interesting

Unfortunately, i also am one of those that cannot understand irreversibility in the basis of a model of elastic balls in a box, specially when i -as others before me during the last 125 years- study the details...

 

[Careful]

Because from initial conditions more reversible physics one does not obtain irreversible equations. This is the reason that nobody can explain the behavior of a dense fluid using reversible dynamics more initial conditions alone. If irreversible phenomena was explained via initial conditions and Newton or Schrödinger equations then would not exist a field of science called non-equilibrium statistical physics, where people want obtain just irreversible equations as those of Boltzmann.

Thanks, that explains everything ! I think I will leave the book of Prigogine where it is By the way, you gave yourself a counterexample through the black hole area arrow of time combined with the Weyl = 0 curvature hypothesis.

 

[Juan R.]

The Weyl = 0 curvature hypothesis is a classical assumption on the initial phase of the universe in a *time reversal invariant* theory (classical GR, so very special intial conditions). This is exactly why this should NOT make you happy ! However, as said before, it is not crystal clear how the horizon area of black holes relates to fundamental degrees of freedom of spacetime (and as such to ``entropy´´ although the similarity is striking). But for sure, the horizon area of black holes gives a deterministic arrow of time.
Cheers,
Careful

Completely wrong!

The Weyl curvature hypothesis is not just about initial conditions. Penrose already wrote about that!

I clearly emphasized

asymmetry on R_{ab}

Not that initial value of R_{ab} was one given

It is just a bit more complex that just initial conditions more reversible equations!

 

[Careful]

Completely wrong!
The Weyl curvature hypothesis is not just about initial conditions. Penrose already wrote about that!
It is just a bit more complex!

No, it is not! The Weyl curvature hypothesis is put in as a constraint on the initial phase of the universe (to explain a uniform big bang) and you should not look for more behind it. In any case, black hole physics still gives me an arrow of time conflicting with your claims Moreover, you cannot speak about an intial value for the ricci tensor since it blows up if you go backwards in time towards the big bang.

 

[Juan R.]

It is really interesting how taking exactly the same initial condition

0--> <--0

and using time simmetric physics, one can obtain (correct)

<--0::::0-->

or (incorrect)

<--0····0-->

Curiously one of those approaches works and the other does not work. An irreversible theory (there are many available on literature) says what is the correct model.

Of course if one constructs an undetailed model

<--0 0-->

one is unable to distinghis from

<--0 0-->

Of course, the claim that irreversibility is solved via initial conditions is a complete nonsense as proven in published literature, many, many decades ago.

 

[Juan R.]

No, it is not! The Weyl curvature hypothesis is put it in as a constraint on the initial phase of the universe (to explain a uniform big bang) and you should not look for more behind it. In any case, black hole physics still gives me an arrow of time conflicting with your claims

Of course that is not about initial conditions

 

[Careful]

Of course that is not about initial conditions

You should not speak about things you do not understand especially towards someone who has spoken about this with the originator himself. Every relativity student understands what I just explained you since it is a mathematical theorem. :zzz: :zzz: Moreover, I am still waiting for your intelligent explanation of the box with two chambers problem (you just said it was not possible).

 

[Juan R.]

You should not speak about things you do not understand especially towards someone who has spoken about this with the originator himself. Every relativity student understands what I just explained you since it is a mathematical theorem. :zzz: :zzz: Moreover, I am still waiting for your intelligent explanation of the box with two chambers problem (you just said it was not possible).

I know rather well i am speaking and this is the reason that i choose specific words. I clearly emphasized asymmetric R_{ab}.

Claim that irreversibility in the School of thinking i said is based in the initial value of the Weyl is simply have no idea of i (or members of that School) was talking. It is rather easy prove that via an initial low value for that Weyl one cannot explain irreversible phenomena or the evolution of universe. In fact, one simply may read published literature.

The trivial model of a box with two chambers already was studied many many decades ago and proved that cannot be explained via reversible Newton equation.

Moreover, I am still waiting for your intelligent explanation of the box with two chambers problem (you just said it was not possible).

[EDIT: unnecessary comments about the intelligence of others deleted]Of course you can (as others) continue thinking that irreversible phenomena is explained via taking the initial state

I have seen your intervention in the thread "Does a controversy still exist ?" where you appears to claim that on your theory light is a classical phenomena. Reading vanesch reply there you, apparently, believe that QM is unnecessary.

Now i understand some replies here...

 

[Careful]

I know rather well i am speaking and this is the reason that i choose specific words. I clearly emphasized asymmetric R_{ab}.

QUOTE]
An assymetric Ricci tensor ?? Now, you must clarify yourself Concerning my distaste for photon like ideas, I a am sure you are aware of the fact that solutions to Maxwell equations can exhibit particle like behaviour. Perhaps this is then not that silly as you ``think´´. To make it easy for you: explain me how it comes that a classical Friedmann universe with some irregular matter grains inside clearly has a dynamical arrow of time while it is a classical solution to GR?

 

[Juan R.]

It is really interesting how taking exactly the same initial condition

0--> <--0

and using time simmetric physics, one can obtain (correct)

<--0::::0-->

or (incorrect)

<--0····0-->

Of course if one writes a nondetailed model then one write just

<--0 0-->

and one is unable to understand i is doing in the simulation. All models of simulation of irreversible phenomena i know are based in curiously irreversible phenomena. Newer the model is reversible. The irreversibility is hidden in one or other way.

Lebowitz -as others before him. claim that "all is initial conditions", but after when one ask to him "explain this phenomena" "obtain this coeficient or this correlation function", then they newer solve Newton reversible equations. They always use equations of motion that are irreversible in one or other way.

But it is important to realize that the Hamiltonian evolution of the system is modified by use of an extra term in the equations of motion on the level of the probability distribution, and not of individual systems. By adding an extra term to the Liouville equation rather than to Hamilton’s equations, the interaction is treated as being of a stochastic nature.

[...]
In principle there are several ways to motivate the extra term in the Liouville
equation. In the first place, it could be motivated from certain assumptions that are of probabilistic nature. In the second place, the extra term could be calculated from the deterministic evolution of the compound system. Bergmann and Lebowitz choose the first option.

[...]
Indeed, from the assumptions they make about the environment
they calculate that not only the fine-grained entropy of the system of interest increases, but also of the compound system. This shows that the final state of the compound system cannot be the result of a deterministic evolution, governed by Hamiltonian forces only.

Of course, the claim that irreversibility is solved via initial conditions is a complete nonsense as proven in published literature, many, many decades ago.

People as Lebowitz claim that all is initial condition but instead of solving Newtonian or Schrodinguer euqation of motion with initial conditions (which does not work) they are forced to write the equation of Newton and add ad hoc additional irreversible terms.

Not only people as Lebowitz claim one thing but after are forced to do other. It is interesting that people who support initial conditions (as the two guys) simply ignore experimental data. The objective of irreversible physics is the description of irreversible phenomena and obiously initial conditions more Newton equations is not sufficient. This is trivial.

The absurd idea irreversibility is an apparent process if one follow a coarse grained approach. That is if one look the macrostates instead of microstates is an authentic absurdity.

A major task for proponents of the coarse graining approach is the justification of the choice of the partition. The size of the cells is usually chosen in correspondence with the limited precision with which points in phase space can be discriminated by means of macroscopic observables. According to Van Kampen, the question how to choose this set is the main problem in statistical mechanics of irreversible processes

A third objection, due to Ridderbos, is that there are cases where the coarse graining approach yields predictions that do not correspond with thermodynamics

Interestingly proponents of the coarse grained approach do not explain why their method fail to explain certain aspects of the spin-echo experiments.

Lebowitz as others claim that all is explain in terms of initial conditions but after in the abstract of his paper on Fourier Law, Lebowitz (with Bonetto and Rey-Belles) writes

This law is empirically well tested for both fluids and cristals [...] There is however at present no rigorous mathematical derivation of Fourier's law for any system (or model) with a deterministic, e.g. microscopic Hamiltonian, evolution

Perhaps by this reason he saw forced to add, ad hoc, an irreversible term to Newtonian equations of motion.

Lebowitz quotes extensively. It is true that Boltzmann said responding to Loschmidt

The sophism now consists in saying that, without reference to the initial conditions, it cannot be proved that the spheres will become uniformly mixed in the course of time.

But Boltzmann is only correct in calling this statement a sophism if the system is really choosing from the available phase space at that time. If the system is obeying hamiltonian mechanics, that is not what is happening.

In fact, the Boltzmann equation is NOT derivable from Newtonian (or Hamiltonian) equations. This was proven many, many, many time ago. In fact, Lebowitz omits to cite the part when Boltzmann recognized that he was used implicit asumptions violating reversible dynamics.

As explained by Brush.

Boltzmann...accepted Burbury's conclusion that an additional assumption was
needed

van Kampen has provided an excellent discussion of the basic
problem of irreversibility in statistical mechanics, and the key elements necessary for its resolution.

In the microscopic complete description the motions of all individual particles
are determined by the familiar differential equations of mechanics… which
are symmetrical with respect to past and future; yet the phenomenological
equations for the macroscopic variables distinguish between past and
future… (This)...makes clear that there cannot be a rigorous mathematical
derivation of the macroscopic equations from the microscopic ones. Some
additional information or assumption is indispensable. One cannot escape
from this fact by any amount of mathematical funambulism.

About Friedman universe. I will say nothing

 

[dgoodpasture2005]

I see a lot of the "the big bang" being discussed here... is this really fair? Everytime we make a more powerful telescope than the last... we set the universes age back a few billion more years... How long before we see nothing? Will we ever? I think time is a ball... not an arrow. But what do i know.

 

[vanesch]

Of course, the claim that irreversibility is solved via initial conditions is a complete nonsense as proven in published literature, many, many decades ago.

Apart stating several times how ridiculous the idea is, and how some others found that a ridiculous idea, I've not learned much. It is not because the problem of deriving phenomenologically correct models corresponding to actual observed numbers is DIFFICULT to do from first principles, and that it is much more EFFICIENT to use irreversible models such as the Boltzman transport equation, that this proves by any account that there MUST NECESSARILY BE irreversibility in the microdynamics in order to observe a macroscopic phenomenology. It does not exclude that either.

Your citations are very one-sided, and inspired by Prigogine's school of thought only. There are also many people who are totally oposed to this view. For instance, Zeh, in his book, "the direction of time" http://www.time-direction.de/ in chapter 3, is not of your opinion. He accepts readily that initial conditions CAN provide for a phenomenological arrow of time in the early part of the evolution - however this then translates in a discussion about how reasonable it is to make this assumption without making the opposite assumption of a special *final* condition.

 

[dgoodpasture2005]

okay this is cooky... but looking back on what i posted... saying that time is a ball... one could make the argument... well if time hasn't reached the beginning of where it started yet... then couldn't we go there, or go back?!(assuming time is traveling in a circle... on the exterior of a circle) ... so i started to think... what if you make the ball smaller and smaller.. 'till this argument dissapears... then time is only a period mark... it's only here and now, there is no past, and there is no future... but it's still circular. So it never ends. I'm not sure I said what I was trying to say.

 

[Juan R.]

It is not because the problem of deriving phenomenologically correct models corresponding to actual observed numbers is DIFFICULT to do from first principles, and that it is much more EFFICIENT to use irreversible models such as the Boltzman transport equation, that this proves by any account that there MUST NECESSARILY BE irreversibility in the microdynamics in order to observe a macroscopic phenomenology.

This -i already said- just prove your misunderstanding on those matters.

Your citations are very one-sided, and inspired by Prigogine's school of thought only.

A simple view i wrote in past posts and you can see that i cited Prigogine but i also cited some other people. Therefore your statement is just false.

There are also many people who are totally oposed to this view. For instance, Zeh, in his book, "the direction of time" http://www.time-direction.de/ in chapter 3, is not of your opinion. He accepts readily that initial conditions CAN provide for a phenomenological arrow of time in the early part of the evolution - however this then translates in a discussion about how reasonable it is to make this assumption without making the opposite assumption of a special *final* condition.

I will simply cite Zeh. One can see how Zeh claims the contrary is saying Lebowitz in above article, for example, and you taked in so early consideration. Remember your past post vanesch!

In contrast to what is often claimed in textbooks, this asymmetric appearance of nature cannot be explained by statistical arguments. If the laws are invariant under time reversal when compensated by another symmetry transformation, there must be precisely as many solutions in the time-reversed class as in the original one (see Chap. 3).

The popular argument that advanced fields are not found in nature because
of their improbable initial correlations is known from statistical mechanics,
but absolutely insufficient (see Chap. 3). The observed retarded phenomena
are precisely as improbable among all possible ones, since they contain
equally improbable final correlations. Their `causal' explanation from an initial
conditions would just beg the question.

The attempt to explain this fundamental asymmetry on the basis of the
`historical nature' of the world, that is, from the assumption that the past
be `fixed' (and therefore neither requires nor allows statistical retrodiction)
would clearly represent a circular argument.

The widespread `double standard' of readily accepting improbable
initial conditions while rejecting similar final ones has been duly criticized by
Price (1996).

Many `foundations' of irreversible thermodynamics are based on a formal idealization that leads to infinite Poincaré recurrence times (for example by using the `thermodynamical limit' of infinite particle number). They are quite irrelevant in our universe of finite age, and they would not invalidate the reversibility objection (or the equilibrium expectation). Rather, they illustrate that some kind of Kaltgeburt is required in order to derive the thermodynamical arrow.

This success [Boltzmann] seems to be the origin of the myth of the statistical foundation of the thermodynamical arrow of time. However, statistical arguments can neither explain why the Stozahlansatz is a good approximation in one and only one direction of time, nor [...]

A new autonomous dynamics has therefore been proposed for S_{cg}, in analogy to the Stozahlansatz, by complementing the Hamiltonian dynamics with a dynamical coarse-graining [...]

In this form it may be also regarded as a variant of the Unifying Principle
thas was proposed by Lewis (1967).

Spin wave experiments also demonstrate that an exactly closed system in
thermodynamical equilibrium may still contain an arrow of time in the form of
`hidden correlations'.

phenomenological master equations such as (3.35) are often understood as describing a fundamental indeterminism that would replace the Hamiltonian dynamics.

The dynamical effect of this formal idealization may be mathematically signalled by a unitary inequivalence between the Liouville equation and the resulting master equation (see Misra 1978 or Mackey 1989).

A fundamental cosmological assumption,

rho_{irrel}(t0) = 0; (3.44)

at a time t0 in the infinite past (similar to the cosmological A^mu_{in} = 0 at the big bang) is therefore quite powerful even though it is a probable condition.

Note that Zeh says 'quite' and note also that is not saying that (3.44) was the origin of irreversibility as you claim.

Moreover, it can be proven that irreversible equation (3.46a) is NOT univocally determined by the initial condition (3.44). In fact, it is easy to prove that (3.44) is compatible with 3.46a and with others equations violating (3.47) and, therefore, incompatible with experimental data. In fact, that proof was done...

Initial conditions are not the basis for understand irreversibility. In fact Zeh also write about this (note the emphasis by the own Zeh).

While the (statistically probable) assumption (3.44) led to the master equation (3.46), it would by itself not characterize an arrow of time.

Therefore, he is just NOT supporting your point. The NOT is rather easy to prove. Initial conditions does not solve the problem of description of irreversible phenomena.

In contrast to the Liouville equation (3.26), the master equation (3.46) or (3.35) cannot be unitary [...]

While a Zwanzig projection can be chosen for convenience in order to derive a master equation (if dynamically consistent), the initial condition must be speciffied as a real condition characterizing this universe.

Of course, that an real initial condition may be specffied but it is also true when one solves Newtonian or Schródinger equations of motion. One chooses the initial condition characterizing the system one is studying. This is independent if process is reversible or irreversible.

However, Zeh cannot argue that initial condition was all we need for obtaining the correct description of irreversible phenomena. In fact, as i stated many times here, the initial condition is compatible with both correct and incorrect equations. And the correct equations are, curiously, those that coincide with the Second law

A low entropy initial state S_0 = 300 at initial instant is not the key to understand irreversibility because one may explain why the observed evolution is always

300 ----> 1000

and is NEWER

300 ----> 100

In both cases, the initial state is the same and one introduces exactly the same initial state when one solves equations for nonconserved observables, for energy, for the correlation functions, etc.

All our models using initial states are reversible if we are studing reversible phenomena (for example Schrödinger equation) or irreversible if we are studing irrreversible phenomena (for example Boltzmann equation, Prigogine equation, Zwanzig master equation, etc.)