博文
与敖平继续讨论统计物理问题【4】
|||
与敖平继续讨论统计物理问题【4】
陈平老朋友来函，感到高兴。
现在附上他的来信和我给陈平的回信
好久没有见过老方了。老兄成果累累，可喜可贺。
这些年，我忙于重建经济学的体系，没有看网络的文献，所以不知网络物理到何程度。
有时间请方锦清到上海来做次讲座，我一定来虚心学习。
我北大已经退休，继续在复旦做研究。所以大部时间在上海。
复旦没和郝柏林联络，据说在做生物学。
以后上海的活动，就请敖平组织了。
我刚到上海，预计7月17日回美。4月15日到英国1周，7月1日到澳大利亚和新西兰10天。
方锦清如来上海，请错过这些时间。
我去北京的时间不定，请方锦清告你的联络方式，有空登门拜访。
对于建体系的问题，我的方式和早期量子力学家类似，即先识别典型实验或案例，
例如行星运动，原子光谱，或布朗运动，
猜可能的解，例如：椭圆轨道，德布罗意波，再建方程，
如方程可以推广到其他案例，是否要对观察对象分类，如生物学分类，运动方程分类，
再思考有无统一理论。
Boltzman 方程是从气体模型导出的，Hamilton 形式是从行星运动和谐振子模型导出的。
薛定谔把生物遗传学的基础建在量子力学上，讨论演化的稳定性有道理，
讨论细胞的形成，就不如钱紘的随机模型。
假如，你得先说服我，为何非物质的网络动力学的行为类似晶体还是流体，还是新的运动形态？
我才会关注你的动力学形式。
经济学的一大问题，是微观经济学套用 Hamilton 形式，结果极糟，不如动力学。
这是我关心的问题：究竟是应该修改 Hamilton 的经济学形式，还是放弃另辟新途？
我的直觉是看生物学能否走通，因为经济学接近生物，而非力学。
因为，数学上构造一个公理体系或形式体系的可能太多了。
离开实验的观察基础，把太多时间投入数学，不是物理学的长处。
我希望读到1篇网络物理的综述文章，从实验结果的分类开始，然后讨论几种理论模型的利弊，
再探讨未来的走向。
最近为了推荐钱紘与敖平的工作，和 Linda Reichl 讨论耗散系统与保守系统之间的边界如何定？
Linda 的回答极为简单，不是普里戈金的大理论，而是实验的观察法：就是看散射。
耗散就是非弹性散射，能量损失，无需引入不确定性，但是时间不对称只是能量损失的结果。不是宏观时空性质，而是相互作用决定。
这在基本粒子和原子物理很好理解，到生物层次看什么？
你在网络系统讨论耗散还是守恒，究竟观察什么？
还没读文章就提要求，似乎太过分了。
问题是，现在信息爆炸，精力有限，只好抓主要的东西。
我凭直觉，觉得敖平的工作非常重要，可能突破 Brussels 学派的局限。
不料老兄的网络动力学也有契机，愿闻以详。
祝好！
陈平
我给陈平的回信：
2012/3/14 fang jinqing <fangjinqing@gmail.com>
陈平：非常高兴得到你的信息。确实多年没有看见了，其实，我不时会想到你呢。去年11-12月我两次到上海复旦大学物理系，一是应邀给物理系“物质科学前沿讲座”报告，讲的就是网络科学的若干前沿课题进展；同时到上海大学去报告；二是参加“复杂系统与经济物理学论坛“，奇怪，你在复旦却不知道，我讲了”经济全球化和网络化下的多层次的高科技网络“。敖教授有精彩报告了。我要是知道你就在复旦大学，我当然会去寻你啊。今年我们什么时候能去上海还不好说，一有好机机会一定拜见你。10月份我去南京参加”第八届全国复杂网络会议“。届时我们再联系。2012/3/13 <aoping@sjtu.edu.cn>
老陈：
请你告诉我：你的上海地址，我可以给你寄一本书：
”网络科学与统计物理方法“
这是毕桥和我的合著，2011年10月，北京大学出版社出版。
该书你可以了解两个课题的联系。这次我们与敖平的讨论也由此展开。
该书你可以了解两个课题的联系。这次我们与敖平的讨论也由此展开。
希望你继续参加讨论。
老方
×××××××××××××××××××××××××××
Hi, Chen Ping:
It is a great coincident that I am discussing similar issues with, perhaps your former colleagues, whom I have not met yet in person, too.
Will send you two such communications. First one is here.
Ping
----- 转发的邮件 -----
发件人: "ping ao" <az5842@yahoo.com>
收件人: "fang jinqing" <fangjinqing@gmail.com>
抄送: "Ping Ao" <aoping@u.washington.edu>, aoping@sjtu.edu.cn, "qiao bi" <biqiao@gmail.com>
发送时间: 星期五, 2012年 3 月 09日 上午 11:25:52
主题: Re: 关于统计物理
Good.
(1) Will hear your critique on our work after you have read them.
(2) If you think Prigogine can do it, it would be nice to learn their work. This would be great for others to learn the power of your approach. In fact, you have not provided their work to show I would be wrong.
And, I would be happy to be shown wrong here.
And, I would be happy to be shown wrong here.
Again, as far as I know, the impossibility for limit circle was stated in their own work.
(3) Yes, I am interested to know the problems solved. In pushing such goal, we may be able to move the field forward.
Pehraps I should state, which I think it is a professional standard when commenting others' work, I have read the major work of Prigogine school.
Of course, I could miss some important their work, which I would be happy to learn.
Of course, I could miss some important their work, which I would be happy to learn.
Ao, Ping
----- 原始邮件 -----
主题: Re: hi, ao ping
Hi, Prof. A. Ping,
(1) Firstly, thanks again for your providing papers, I have gotten them. I will read them, and discuss with you for some interested problems.
(2) I don't know whether or not that the Prigogine school can do pdf (2), but subdynamics is efficient to any linear operators, with quite flexible fashions, so let me firstly see your models and achievements, then see whether subdynamics could do something. Except subdynamics, there are other methods in Pregogine school, such as internal time operator methods, resolvent operator plus extending functional space approaches, etc. I don't know how do you get a conclusion that "As far as I know, this was also regarded impossible by Prigogine school". Of course I hope that you could be happy to be corrected in the future by some progresses of subdymaics or other methods from me. By the way, subdynamics has gotten many important results and predictions. Partly, you can see in the third part of the book of me and Prof. Fang, and also can see many papers from Petrosky, Anttoniou, etc, which you can find part list of them in the references of the book. In the books of Balescue he also gave many results and predictions.
(3) But in this stage, as you said the intention of you (also including me) is not to argue which approach would be better. I absolute agree with this point. Actually, any method if it existed a long time, then there is reason or righteousness for its existence. Our goal is the same, that is try to achieve more important progresses for non-equilibrium statistical physics, for China and for the world.
(2) I don't know whether or not that the Prigogine school can do pdf (2), but subdynamics is efficient to any linear operators, with quite flexible fashions, so let me firstly see your models and achievements, then see whether subdynamics could do something. Except subdynamics, there are other methods in Pregogine school, such as internal time operator methods, resolvent operator plus extending functional space approaches, etc. I don't know how do you get a conclusion that "As far as I know, this was also regarded impossible by Prigogine school". Of course I hope that you could be happy to be corrected in the future by some progresses of subdymaics or other methods from me. By the way, subdynamics has gotten many important results and predictions. Partly, you can see in the third part of the book of me and Prof. Fang, and also can see many papers from Petrosky, Anttoniou, etc, which you can find part list of them in the references of the book. In the books of Balescue he also gave many results and predictions.
(3) But in this stage, as you said the intention of you (also including me) is not to argue which approach would be better. I absolute agree with this point. Actually, any method if it existed a long time, then there is reason or righteousness for its existence. Our goal is the same, that is try to achieve more important progresses for non-equilibrium statistical physics, for China and for the world.
Best Regards,
Biqiao
On Tue, Mar 13, 2012 at 8:51 AM, < aoping@sjtu.edu.cn > wrote:
Dear Prof. Bi and Fang:
In response to the inquiry for our construction of potential function in generic situations, here I list our key technical work here, which I didn't in my prevous message.
The pdf of 2) is attached here, which deals with a situation most people in nonequilibrium thought not possible: Existence and construction of potential function in limit cycle dynamics.
The potential function has all the properties in physics.
As far as I know, this was also regarded impossible by Prigogine school (I would be happy to be corrected).
The pdf of 2) is attached here, which deals with a situation most people in nonequilibrium thought not possible: Existence and construction of potential function in limit cycle dynamics.
The potential function has all the properties in physics.
As far as I know, this was also regarded impossible by Prigogine school (I would be happy to be corrected).
1) On the Existence of Potential Landscape in the Evolution of Complex Systems,
P. Ao, C. Kwon, and H. Qian, Complexity 12 (2007) 19-27.
http://arxiv.org/PS_cache/q-bio/pdf/0703/0703044v1.pdf
P. Ao, C. Kwon, and H. Qian, Complexity 12 (2007) 19-27.
http://arxiv.org/PS_cache/q-bio/pdf/0703/0703044v1.pdf
2) Limit Cycle and Conserved Dynamics,
X.-M. Zhu, L. Yin, P. Ao, Int. J. Mod. Phy. B20 (2006) 817I h-827.
http://ejournals.wspc.com.sg/journals/ijmpb/20/2007/S0217979206033607.html
X.-M. Zhu, L. Yin, P. Ao, Int. J. Mod. Phy. B20 (2006) 817I h-827.
http://ejournals.wspc.com.sg/journals/ijmpb/20/2007/S0217979206033607.html
3) Structure of Stochastic Dynamics near Fixed Points,
C. Kwon, P. Ao, and D.J. Thouless,
Proc. Nat’l Acad. Sci. (USA) 102 (2005) 13029-13033.
http://www.pnas.org/content/102/37/13029.full.pdf+html
C. Kwon, P. Ao, and D.J. Thouless,
Proc. Nat’l Acad. Sci. (USA) 102 (2005) 13029-13033.
http://www.pnas.org/content/102/37/13029.full.pdf+html
4) Potential in Stochastic Differential Equations: Novel Construction,
P. Ao, J. Phys. A37 L25-L30 (2004).
http://www.iop.org/EJ/abstract/0305-4470/37/3/L01/
P. Ao, J. Phys. A37 L25-L30 (2004).
http://www.iop.org/EJ/abstract/0305-4470/37/3/L01/
Again, my intension here is not to argue which approach would be better.
Rather, I wish to stimulate the research in China to seize a unique opportunity to make lasting contribution.
My feeling is that, this is also the gaol in your 2010 paper on network science and statistical mechanics.
Rather, I wish to stimulate the research in China to seize a unique opportunity to make lasting contribution.
My feeling is that, this is also the gaol in your 2010 paper on network science and statistical mechanics.
Look forward to hearing your feedback.
Best,
Ao, Ping
----- 原始邮件 -----
发件人: "ping ao" < az5842@yahoo.com >
收件人: "qiao bi" < biqiao@gmail.com >
抄送: "fang jinqing" < fangjinqing@gmail.com >, aoping@sjtu.edu.cn
发送时间: 星期二, 2012年 3 月 13日 下午 1:33:32
收件人: "qiao bi" < biqiao@gmail.com >
抄送: "fang jinqing" < fangjinqing@gmail.com >, aoping@sjtu.edu.cn
发送时间: 星期二, 2012年 3 月 13日 下午 1:33:32
主题: Re: hi, ao ping
Dear Prof. Bi:
Thanks for your interesting questions.
See my response in the context below.
Ao, Ping
From: qiao bi < biqiao@gmail.com >
To: ping ao < az5842@yahoo.com >
Sent: Tuesday, March 13, 2012 11:13 AM
Subject: Re: hi, ao ping
To: ping ao < az5842@yahoo.com >
Sent: Tuesday, March 13, 2012 11:13 AM
Subject: Re: hi, ao ping
Hi， Prof. A. Ping，
(1) I think the potential function is not only the Hamiltonian in the non-equilibrium situation, question is what is its rigorous math. and phys. meaning?
Yes, it is rigorous math, with all the usual physics meaning. In fact, the latter is its big merit of our approach, comparing with those previous proposals.
Could you give more clear description to it in the non-equilibrium situation?
Yes, it is rigorous math, with all the usual physics meaning. In fact, the latter is its big merit of our approach, comparing with those previous proposals.
Could you give more clear description to it in the non-equilibrium situation?
A good place to get a start on our approach is the paper sent you early:
Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics,
P. Ao, Communications in Theoretical Physics 49 (2008) 1073-1090.
http://ctp.itp.ac.cn/qikan/Epaper/zhaiyao.asp?bsid=2817
Let me know if you have any questions on it.
Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics,
P. Ao, Communications in Theoretical Physics 49 (2008) 1073-1090.
http://ctp.itp.ac.cn/qikan/Epaper/zhaiyao.asp?bsid=2817
Let me know if you have any questions on it.
(2) You said there is a candidate tentatively named Darwinian dynamics for non-equilibrium statistical physics , many thanks for your message and works although in this stage I am not sure about this, but I am interested to study. How about it is related to the negative entropy?
As you may observe from above paper, the connection to the negative entropy ( not a good term in my opinion) should be simple, because both energy and usual entropy are naturally in our framework.
Which kinds of parameters can generally determine the potential function in a non-equilibrium statistical system?
There is NO need for additional parameters.
There are lots of confusions in literature on non-equilibrium statistical system, which we can discuss more later.
In our framework, potential function (or Hamilonian, depending on context) is a necessary concept to describe such systems.
(3) About chaotic map related to the complex spectral decomposition of koopman operator which is not Hamiltonian operator, if there is no the concept of extension Hilbert space, the Feymann approaches could be very difficult, this may be a reason there seems be no one has done these before. So, I am not sure Feymann approach could do it except using some extension tech. of Hilbert space, if that sort of extension happens, that would be exact what I said meaning of "did correct calculation then get the same result", which implying "extension".
There are lots of confusions in literature on non-equilibrium statistical system, which we can discuss more later.
In our framework, potential function (or Hamilonian, depending on context) is a necessary concept to describe such systems.
(3) About chaotic map related to the complex spectral decomposition of koopman operator which is not Hamiltonian operator, if there is no the concept of extension Hilbert space, the Feymann approaches could be very difficult, this may be a reason there seems be no one has done these before. So, I am not sure Feymann approach could do it except using some extension tech. of Hilbert space, if that sort of extension happens, that would be exact what I said meaning of "did correct calculation then get the same result", which implying "extension".
Path integral can be, and have been extended, to discrete situations.
It would be an interesting project for students to construct the potential function or Hamilotnian out of dynamical processes described by koopman operator.
(4) But of course I don't think it is completely the same as subdynamics, but they may be the same in some crossing field. If you have great passion to study the both differences during recent time, that is welcome, but I would point out, I don't think the power of the Feymann approaches can be beyond any kind of (famous) projected operators approach such as Ziwanzig projected method, but the subdynamics is for beyond. Therefore for me here there is no big apple even if I can find some differences. I am sorry I said this, which seems too proud, and hope you could not misunderstand I am against you to do this or any no respect to the Feymann approaches, because I only want to point the fact that has been tried and done by the Brussels school in past 30 years. Several hundreds papers have been published, which should be evidences to allow you see the both differences if you have enough time.
As far as I know, subdynamics has not yielded new physics predictions yet. Most work is on mathematics side.
I can be wrong on this, due to my limited knowledge. Will be happy to be corrected.
On the other hand, there are quite a few new predictions from Fyenman type description of subsystems.
No, I am not keen to find the difference, either.
One reason is that, when coming down to real physics problems, subdynamics usually involves approximations at very early stages.
In conclusion, named Darwinian dynamics is more meaningful, I hope having further understanding and discussion with you, a nd hope subdynamics or some new progresses can in principle be tested experimentally from the Darwinian dynamics or evolutions .
It would be an interesting project for students to construct the potential function or Hamilotnian out of dynamical processes described by koopman operator.
(4) But of course I don't think it is completely the same as subdynamics, but they may be the same in some crossing field. If you have great passion to study the both differences during recent time, that is welcome, but I would point out, I don't think the power of the Feymann approaches can be beyond any kind of (famous) projected operators approach such as Ziwanzig projected method, but the subdynamics is for beyond. Therefore for me here there is no big apple even if I can find some differences. I am sorry I said this, which seems too proud, and hope you could not misunderstand I am against you to do this or any no respect to the Feymann approaches, because I only want to point the fact that has been tried and done by the Brussels school in past 30 years. Several hundreds papers have been published, which should be evidences to allow you see the both differences if you have enough time.
As far as I know, subdynamics has not yielded new physics predictions yet. Most work is on mathematics side.
I can be wrong on this, due to my limited knowledge. Will be happy to be corrected.
On the other hand, there are quite a few new predictions from Fyenman type description of subsystems.
No, I am not keen to find the difference, either.
One reason is that, when coming down to real physics problems, subdynamics usually involves approximations at very early stages.
In conclusion, named Darwinian dynamics is more meaningful, I hope having further understanding and discussion with you, a nd hope subdynamics or some new progresses can in principle be tested experimentally from the Darwinian dynamics or evolutions .
There are now new experiments to test some of our predictions. For example, as mentioned to you in previous messages, we predict that a new type stochastic integration is needed.
A recent experiment does show that the usual Ito and Stratonovich types are not valid. Instead, a special case of prediction is valid.
Best Wishes,
A recent experiment does show that the usual Ito and Stratonovich types are not valid. Instead, a special case of prediction is valid.
Best Wishes,
Biqiao
On Fri, Mar 9, 2012 at 10:39 PM, ping ao < az5842@yahoo.com > wrote:
Dear Prof. Bi:
Thanks for the good questions.
(1). Potential function in our work is indeed, or play the samilar role as, the Hamiltonian in physics, whether or not in equilibirum or not.
Because we need broader dynamical description, what we have shown is that, even in biological, social and other situations, "Hamiltonian" exists.
Such existence guarantees that statistical mechanics type decription can be used in those fields, as, of course, people have been doing successfully so far, though they have not understood the keys yet.
(2) I do not know your definition, hence I cannot say anthing.
On the other hand, the potential function in our work is both dynamical and statonary quantity, exactly the same situation in usual physical systems.
(3) I agree that Feynman type description has its advantages but I am no interested in defending such approach.
I think it is most interest to see whether or not there are any differences in physics: For a given situation, whether or not two approaches would give different predictions. Or, they would be completely equivalent. From a physicist's pespective, I am not sure of the last point.
For technical mathematical problems, such as you posted, can the Feymann approach solve complex spectral problems for chaotic maps?
while I do not know anyone has done that, I believe the answer is yes, Feynman approach can do that. The reason for such assertation is actually simple: Feynman's path integral is a general mathematical framework.
Again, I am more interested in situations which can in principle be tested experimentally.
Ao, Ping
From: qiao bi < biqiao@gmail.com >
To: ping ao < az5842@yahoo.com >
Sent: Saturday, March 10, 2012 5:21 AM
Subject: Re: hi, ao ping
To: ping ao < az5842@yahoo.com >
Sent: Saturday, March 10, 2012 5:21 AM
Subject: Re: hi, ao ping
Hi, Prof. A. Ping,
(1) (1) The potential function is quite interested in the Darwinian dynamics, since it can consist of a formula for the canonical ensemble. I understand this formula is correct even for non-equilibrium states in the Darwinian dynamics. Could you give more clear description to the potential function? I believe it is just Hamiltonian in the equilibrium situation, but what is exact meaning in the non-equilibrium situation?
(2) (2) I firstly guess: the potential function = the potential of information density, which may be related to my recently work (J. Phys. A in submission). But I hope this statement will be explained after I truly understand the potential function.
(3) (3) Feymann types of approaches have advantages, especially to the quantum field system, but I believe that if we did correct calculations the subdynamics and the Feymann methods will give the same results. However, I said the correct calculation is not that kind easier, since it needs researchers to have enough skills to handle both sides. Many cases, because implied not correct calculation, we did the wrong result. Furthermore, subdynamics has introduced many new concepts, such as the extension Hilbert or Liouville space, the complex spectral decomposition, the similarity non-unitary transformation, and the differential kinetic equation to the projected density operator and so on, these new concepts have appeared in the subdynamics both in classical and quantum situations to lead it as a candidate to unify equilibrium and non-equilibrium statistics, while in the Feymann formalism my level cannot see this possibility. For example, can the Feymann approach solve complex spectral problems for chaotic maps? Subdynamics is useful to any linear operators not only Hamiltonian or Liouvillian. So in this period, for saving time, I suggest to first consider the Darwinian dynamics, because it may be more meaningful. I think you more know this.
Best Wishes,
Biqiao
(1) (1) The potential function is quite interested in the Darwinian dynamics, since it can consist of a formula for the canonical ensemble. I understand this formula is correct even for non-equilibrium states in the Darwinian dynamics. Could you give more clear description to the potential function? I believe it is just Hamiltonian in the equilibrium situation, but what is exact meaning in the non-equilibrium situation?
(2) (2) I firstly guess: the potential function = the potential of information density, which may be related to my recently work (J. Phys. A in submission). But I hope this statement will be explained after I truly understand the potential function.
(3) (3) Feymann types of approaches have advantages, especially to the quantum field system, but I believe that if we did correct calculations the subdynamics and the Feymann methods will give the same results. However, I said the correct calculation is not that kind easier, since it needs researchers to have enough skills to handle both sides. Many cases, because implied not correct calculation, we did the wrong result. Furthermore, subdynamics has introduced many new concepts, such as the extension Hilbert or Liouville space, the complex spectral decomposition, the similarity non-unitary transformation, and the differential kinetic equation to the projected density operator and so on, these new concepts have appeared in the subdynamics both in classical and quantum situations to lead it as a candidate to unify equilibrium and non-equilibrium statistics, while in the Feymann formalism my level cannot see this possibility. For example, can the Feymann approach solve complex spectral problems for chaotic maps? Subdynamics is useful to any linear operators not only Hamiltonian or Liouvillian. So in this period, for saving time, I suggest to first consider the Darwinian dynamics, because it may be more meaningful. I think you more know this.
Best Wishes,
Biqiao
On Wed, Mar 7, 2012 at 10:55 PM, ping ao < az5842@yahoo.com > wrote:
Dear Prof. Bi, Qiao:
Let me know if you have not received the 6 paper which you are interested in.
(2) The rigorous approach of Lebowitz and Feynman is completely based on (accepted) quantum mechanis.
Indeed, it generates, in general, a differential and integral equation for sub-system dynamics. It would be interesting to know the samilarity and difference from the differential equation in your subdynamics. In particular, it would be great interest to see whether or not there are differences in physics predictions in some situations.
If there would be no difference in physics, differential equations are indeed usually easier to handle than differential-integral equations.
(3) Two Leggett's representative work in this direction are, if it may be helpful:
A. O. Caldeira and A. J. Leggett, Ann. Phys. (N.Y) v.149, 374 (1983);
A.J. Leggett, et al. Rev. Mod. Phys. v.59, 1 (1987)
Unfortunately, I am not accessible to their pdf files right now.
(4) My 1999 PRB paper with Zhu is on the correct treatment of vortex dynamics, sent you in previous message ( iii) paper ) .
Nonlinear phenomena have emerging entities, such as topological defects (vortices, magenetic monopoles, fractional charges, etc) and solitons.
In my experience, straightforward extension of Green's function from linear limit can be dangerous and can easily lead to incorrect results.
Will be happy to discuss with you what I know.
(5) Darvinian dynamics may be viable candidate for the foundation of nonequilibrium processes.
It naturally contains the idea of (canonical) ensemble.
In my view, the micro-canonical ensemble has nothing to do with stastical mechanics.
It is pleasure to find an active group of scientists in China working on such fundamental and pratically very useful problems.
Best,
Ao, Ping
Click here to Reply, Reply
https://blog.sciencenet.cn/blog-266190-547717.html
上一篇：与敖平继续讨论统计物理问题【3】
下一篇：与敖平继续讨论统计物理问题【5】
