Letter ##1: 15 January 2004 (partial)

Dear Dr. Rondoni,

.......................

Please note that I am asking for a clear statement about your opinions or results on OUR paper or that you attribute to us .....

Please note that from now on I WILL MAKE PUBLIC your answers via my web page: therefore, please, write in english.

...........

Sincerely GG

Letter ##2: 15 January 2004 (verbatim, reply to 1) From: Lamberto Rondoni

Dear Giovanni,

I hope this will help clarify the situation once and for all. If it doesn't, and I think e-mail is not the best way of solving this problem, we will have to think of other ways of proceeding. I take this opportunity, however, to apologize to anyone to whom I may have caused any incovenience.

>>From your letter of yesterday evening (in italian) and from at least

> another letter (in english) that you wrote yesterday I understand

>

> 1) you have withdrawn your cond-mat/0312353 paper from the archive

This is correct.

> 2) in spite of your acknowledgements (in italian) that all the

> statements in cond-mat/0312353 about the work of

> Prof. Cohen and me that I had challenged were, in fact, incorrect

> you are keeping the submission of cond-mat/0312353 to PRE running

> and waiting for referee reports

Yes. The journal indicates that the referees have recevied the paper some time ago. They most likely have already noticed and written up things which we would prefer to avoid in the future. This would spare the referees from working twice on the same issues. I do not think that it would be a responsible thing to withdraw the paper from the journal at this stage. But that paper will not be resubmitted. I made this clear in our correspondence.

However, I must explain that I never acknowledged that the content of our paper was incorrect. That may well be the case, and I am ready to acknwoledge it, if that is the case.

I acknowledged the fact that the paper was incorrectly formulated.

A new paper should express better our views, and then it will become clear whether the content of this paper is correct or incorrect.

> 3) unlike what you wrote me, you are still convinced that your paper

> is "basically correct" and that you derive this feeling (? or

> certainty ?) from a discussion with Prof. Ruelle, as you wrote

> yesterday.

> In fact I see no other reason to keep the paper under review

I explained why we keep the paper under review. It is because we believe that it has been partly or fully reviewed. However, I have explained in my past e-mails that this paper will not be resubmitted. A new paper is being written now.

Yes, I got the impression that the content of our (incorrectly formulated) paper may be correct. I got this from various sources, including my correspondence with Prof. Ruelle. If I misunderstood anyone's remarks, I am sorry. But, certainly, I did not want to use their words to claim that my paper is correct, especially if they don't think so. I only expressed what I believe from what I have gathered. I mentioned my correspondence with Prof. Ruelle, in my e-mail to Prof. Cohen, only because he knew of it. But I did not say that Prof. Ruelle had told me that the paper is correct. If I used Prof. Ruelle's words improperly, that was unintentional, and I am sorry for that.

Whether the content of this paper is correct or not, will have to be judged when the, hopefully correctly formulated version, will come out.

> I am, of course, very interested in discussing your claim with

> Prof. Ruelle himself. I am at the moment in Paris and this is an

> opportunity that I do not want to miss. Particularly as you are asking

> me (in italian) to help you in making your paper "less offensive" (as

> you may imagine I think instead that, after your own admissions (in

> italian), a more appropriate wording would be "less wrong" also

> because I am not at all offended).

This is a relief for me. I thought otherwise.

> Please send me the exact conclusions that you claim to have followed

> from your correspondence with Prof. Ruelle which make your statements

> about the work by Prof. Cohen and me, or by me, still "basically

> correct" in your paper which, as the title itself makes clear, is

> mainly about our work.

My impression is that there are some molecular dynamics models which do not satisfy the Chaotic Hypothesis or that do not satisfy the fluctuation relation of the Gallavotti-Cohen theorem. To explain this point is the only purpose of our paper, and the idea comes in part from my correspondence with Prof. Ruelle. But it has other motivations as well.

This impression may be right or wrong, but I have been told that the old paper didn't make this point. I was told that that paper claimed we had found mistakes in the existing proofs of the Gallavotti-Cohen theorem.

This was not the point we wanted to make. Therefore, we are preparing a new paper for the scientific community to judge. If our point turns out to be wrong, I will gladly acknowledge that.

> After the letters that you sent around (at least those that, once more

> being in italian, you sent only to an apparently selected audience) I

> am confident that you realize that if your paper is "basically

> correct" (as you write to some, in english) this means that the work

> by Prof. Cohen and me is basically wrong: I refer for instance to the

> comments in the abstract and to the statements in appendix B (only to

> fix the ideas, as you know from my previous letters).

I have sent the e-mails in italian only doing a reply-all. If I should have not done so, I am really very sorry. But I thought it would be all right. I did not see any reason for sending these e-mails to others. But of course, as acknowledged also in my e-mails, I had had some correspondence with others.

In any event, I do not understand why you say that if I am right, you must be wrong. I don't see any reason for that. You, Prof. Cohen, Prof. Ruelle and others have proven a theorem under some assumptions. The theorem is definitely correct. But I ask the question of which systems fit the assumptions, and which do not. That is all.

I don't see how this could imply that you did any mistake.

Now, I acknowledged that the old paper did not say this correctly, that its formulation could upset and offend some people. I apologized, and apologize for that. It was wrong on my side to write something that suggested that you made any mistake. For that reason, the paper has been withdrawn, and will not be resubmitted. If there is anything else I should do, please let me know.

> Please note that I am asking for a clear statement about your opinions

> or results on OUR paper or that you attribute to us: the SAME

> comments, PLEASE, that could be presented to me, to prof. Cohen, to

> prof. Ruelle as well as to interested colleagues. Science should not

> depend on the language one uses.

I agree. Your results are correct. If I suggested a different view, that is because I did not express my views correctly. I hope I have been clear enough now.

> Please note that from now on I WILL MAKE PUBLIC your answers via my

> web page: therefore, please, write in english. I feel forced to do so

> as you write different statements to different colleagues (in

> different languages) and confusion is increasing and most people

> cannot take the time to check what is true and what not.

This is fine with me. I hope I made clear the source of the misunderstandings. In a few words, what I wanted to say was:

You did not make any mistake. I agree that my paper was incorrectly formulated, but, at the same time, I believe that the point in it is correct. When the new paper will be ready, you and anyone will be able to judge.

I hope this helps

My best regards

Lamberto

--------------------------------

Lettera ##3: From Giovanni Gallavotti, 15 gennaio 2004

Dear Dr. Rondoni:

I pick up two points in your letter below which refer to your paper 0312353.pdf (still submitted to PRE)

>Whether the content of this paper is correct or not, will have to be judged >when the, hopefully correctly formulated version, will come out.

I say that if you are right our work must be wrong because you say in the abstract that our theorem predicts an unsymmetric relation in the hamiltonian case. This can be judged now.

I say that if you are right our work must be wrong because you attribute to the papers [4] a result, p. 30, that is the basis of the criticism mentioned in the abstract.

>However, I must explain that I never acknowledged that the content >of our paper was incorrect. That may well be the case, and I am >ready to acknwoledge it, if that is the case.

therefore I say that if you believe, as you write, that the content of your paper is still correct then we are wrong (see above).

Question:

Do you now acknowledge that the abstract of your paper and your related claims about our work are wrong ? I thought you had done so in your letters in italian: if so little is left of the paper if I understand it.

I am sorry to ask that: but you distributed your paper to the world stressing that we were predicting things we did not! and after 20 days you still do not want to acknowledge that; and in fact you keep your paper under refereeing.

Sincerely: GGallavotti ps I attach a copy of your paper where you can check my statements.

Lettera ##4: (From F. Bonetto)

Dear all

I'm trying to follow the discussion. I do agree with Giovanni that the paper is written in a terrible way and that many of the statement it makes are wrong. On top of this the work of GC is misquoted and the use of term like theorem or hypothesis is highly confusing.

I just want to try to understand what was the point of the authors in writing this paper. They are, in my opinion, good scientists and so I belive they had an idea that they probably expressed in a wrong and confusing way may be helped by some personal animosity.

In what follows I try to paraphrase their point as I understand it. Please correct me if I make mistakes.

The FT, has any theorem, is composed by some hyptheses from which a thesis follows. The hypotheses are chaoticity (Anosov), reversibility and that the large deviation functional for the phase space contraction is analytic in the intervall [-p^*,p^*] and the average of the large phase space contraction is positive. The corresponding thesis is the usual large fluctuation simmetry.

Clearly the thesis of a theorem can be verified also when the hypotheses are not verified. This is the content of many numerical works where one sees that the fluctuation relation (so I call the thesis of the FT) holds in systems that are surely not anosov (in the mathematical acception of the term). E.g. the several biliards we studied where the dynamics is not even continuous.

The above mentioned numerical results have been used to "invert" (note the quotation mark) the FT. I mean that the fact that the fluctuation relation (FR) is verified is an inderect evidence that the systems under consideration behave as if they were Anosov. This in turn give confidence that the theses of other theorems (e.g. GK formula) proven in the Anosov setting (which hipotheses are not verified for the systems under consideration) may turn out to be verified. This more or less what the authors call Chaotic Hypothesis.

Thus it may be interesting to look for systems that although chaotic in some weak sense (e.g. existence of one positive Lyapunov exponent) do not satisfy the FR. Note that asking whether the FT is correct for this systems makes no logical sense. The author start with the question: what about a reversible Anosov system where the average phase space contraction is 0 but the sup of the time average of the phase space contraction on a trajectory of lenght t is bounded away from 0 uniformely in t. This mean that we can find points for which the time average of the phase space contraction for an infinite time on the trajctory issuing from that point is non 0. The argument goes on saying that, from the proof of the theorem (? which?) follows that one can identify p^* with the above mentioned maximum of the time average of the phase space contraction. This seems to lead to a contradiction.

Clearly no contradiction is present. I think that this is due to theorem 6.4.3 of the book by Gallavotti Gentile and myself from wich it follows (I belive) that no such system can exists. But it is also possible that the above identification of p^* with the maximum time averaged entropy production is not correct. In any case it would be interesting to see if such Anosov systems exists.

Clearly if one relaxes the Anosov condition it is easy to find example where the maximum of the time averaged entropy production is non 0, endeed infinite, but the average is 0. This is for example the case I discussed in my previous mail where you have 2 particles in a biliard interacting through a potential and an isokinetic thermostat. In this case the average phase space production on a trajectory is the potential difference between the initial and the final point. This implyes that the probability of seeing an average phase space contraction larger that a given S is given by the SRB probability of the set of points where the potential is larger than S. If the potential is not bounded any value S can be observed. Moreover one can add an external electric field (and some obstacles to avoid trivial motion) to the two particle to create a non zero phase space contraction. These seem to be the systems that the authors have in mind.

These systems represent flows that are clearly not Anosov. Indeed the dynamics is syngular (as it immediatly follows form the fact that a regular function on a compact set is bounded). Is the FR (again not the FT, the systems are not Anosov) verified for these systems? the question is interesting and seems that is has been addressed in some numerical works with a negative answer. This is justified by the fact that the FR cannot hold at 0 external field so that it will not hols at small external field. I had no time to check those works but I'm a little surprised for the following reason. I can chose as a poincare' section for the above flows the surface defined by the fact that the to particles are at a given (small distance) and their distance is increasing. I can call such a situation an (after)collision. If I look at the dymanical system generated by the intersection of the flow with this poincare section I have that the phase space contraction between two collisions is always bounded. I would be very surprised if the FR resulted to be wrong for this (descrete time) dynamical system. This should be easy to check to whoever did the previous simulation.

My impression is that the presence of the singularitites make it necessary to go to very long time to see the FR for the above systems in continuum time. And the lenght of time needed diverges with the smallness of the external field. I think I have an argument for this that I can give you if you are interested. So I tend to think that the difficulties in seeing the FR in the numerical work for the above system are due to simulation not long enough. But this is only an intuition.

I'm sorry for the long mail but is was useful at least to me to understand discussion. I would like to ask Lamberto if he agrees that this is the content of their paper, at least very schematically.

Best Federico

P.S.: I think we used the two different expression FT (fluctuation theorem) and FR (fluctuation relation) in the paper with Joel and Kolia really to avoid some of the confusions we are discussing about now.

Letter ##5: From Dr. Rondoni Fri Jan 16 10:23:08

Dear Giovanni,

I think Federico's e-mail clarifies the situation in all its aspects. I only repeat once more that our paper has been withdrawn because we understood, thanks to your observations, and those of others, that it made incorrect statements (even if it was not our intention to do that).

My best regards

Lamberto

Lettera ##6: Reply to #5, 16 Jan 2004

Dear Dr. Rondoni

NOTHING IS CLARIFIED!! In fact the letter by Bonetto shows that you are wrong if you agree with it.

PLEASE answer the questions: I asked. Is your paper correct in attributing the theorem in appendix B to GC?

If not is the theorem correct?

I claim that is is NOT. If so your paper is wrong (and I do not understand why you keep its submission) otherwise my work is wrong. If it is correct but not proved by us please tell me where is it proved.

You cannot play with the words: your paper has not been withdrawn; it is still submitted to PRE. Please do a scientific discussion based on logical assertions. After you wrote that all my work is wrong I have the right to know why.

Sincerely: GGallavotti

Letter ##6: 17 Jan 2004 (answer to the previous + my reply)

Dear Giovanni,

I do not know what to say more. If the paper has been withdrawn it does not exist any more. You insist to say that this nonexisitng paper told that all your work is wrong. So let me make it clear:

YOUR WORK IS RIGHT

Clearly, a different interpretation of my paper was possible. Therefore, the paper has been withdrawn. I have also acknowledged that I made a mistake in not realizing that our paper could be read the way you did. I already said that it made incorrect statements.

I really don't know what else I could say about a nonexisting paper.

Now, you insist that the paper exists because is under review. I explained that we don't to waste the referees' time. We think this is the most responsible attitude. But we may be wrong. If you have something better to suggest, please let us know. I hope you are not bothered by the thought that we may not do as we promised, resubmitting the paper.

My best regards

Lamberto

-------------------------------

Reply

Dear Dr. Rondoni

Please ANSWER (once and for all) the questions I asked: you are avoiding them.

You write that we have proved a theorem (Appendix B):

is the theorem really proved by us?

where?

if not by you? and

where is the proof?

The theorem is WRONG as I wrote you, and it is the basis of many critiques to the work of CG in your paper (eg abstract). As a consequence I want to know why you say that you have not made mistakes and why you believe that CG is correct if you think that it contains that theorem. PLEASE answer.

I am afraid that I do not understand why you keep the paper on PRE if it is wrong.

Sincerely: GGallavotti

ps: the paper HAS NOT been withdrawn: as you say it is still submitted to PRE! please use language appropriately In any event it is still on my web page.

Letter ##7: Friday 16 January 2004 and answer

Dear Giovanni,

I really hate to upset you. Simply I thought that I had answered your questions. That's all. I'll try again.

It is true that in the paper we have discussed, the terms Gallavotti-Cohen FluctuationTheorem, or GCFT, were misused. When they appeared in the text they incorrectly referred to your theorem. They meant to refer to your theorem, but your theorem had not been correctly reported in that paper.

Had that paper been formulated more precisely, it would have been obvious that it contained no critique of your work.

I have acknowledged that to read that paper as a critique of your work was possible. But the paper has also been withdrawn from the archives.

As to the PRE submission, I explained my reasons. But I am ready to listen, if you have better suggestions. As far as I am concerned, it would be irresponsible to withdraw the paper from PRE at this stage. However, if you strongly feel that it would be better to withdraw it as soon as possible from PRE, I will consider this option with my co-authors.

I hope this answers your questions

Best regards

Lamberto

---------------------------- Answer

Dear Dr. Rondoni

I have no suggestion on what you should do about your paper. In fact I really hope that your paper will be published as it is now so that I can comment on it in front of a wider audience. I only mentioned the improper use of the word "withdraw" because you seem to be playing with words (here as well as elsewhere) and I find that insulting.

What I am concerned with is: YOU DO NOT ANSWER. You say that your paper is correct: hence the theorem in appendix B that you atrribute to us. But that theorem is false. I asked

1) where did we prove the theorem?

2) if we did not then ou proved it? if so your paper s wrong and you should acknowledge because that is the basis of your statements about our work?

PLEASE ANSWER once and for all. I am not upset: I think that you are not behaving appropriately. I remind you that I claimed that your paper (hence a large portion of it) is WRONG and that you denied that: hence I have the right to an answer to the above questions.

Sincereley: GGallavotti

Lettera ##8: From rondoni@calvino.polito.it Sun Jan 18

Dear Giovanni,

> I thought that what I told you clearly meant that the paper we discussed must be wrong, one way or another (at least, this is my opinion).

In my previous e-mails, I did an effort to explain what I meant by wrong in that specific case, addressing the issues that you had raised. For instance, you asked about appendix B, and I acknowledged that incorrect (wrong) statements reported in that appendix were incorrectly attributed to you (being incorrect, of course, nobody could have proved them). This was part of of my previous e-mail. In another e-mail you pointed out that that paper accused you of having done some mistake; then I explained that if that was the case, it was due to improper (wrong) formulation of our ideas, as, in reality, you had done no mistake.

> However, if you feel that this is playing with words, and you only want to hear the word "wrong", with no explanation, that is also fine.

In my opinion, that paper was WRONG.

> And indeed it has been withdrawn form the archives, and will not be resubmitted to PRE.

I sincerely hope that I have satisfied you with my answer, this time.

My best regards

Lamberto

-----------------------------------------------

I stop the discussion here as I see no point continuing it: hopefully this will have contributed to clarify the relationship between the work of CG, criticized in the paper cond-mat/0312353 and others, see also J. Stat. Phys.96, 1343--1349, 1999

GG