In a simple Ising model example, the quadratic terms can be thought of as edges in an undirected graph. Depending on which J values are zero, there can one phase space or many independent phase spaces depending on how many disconnected components there are.
A real material would be subject to environmental magnetic fields and would also require a more complicated energy function with terms for other axes. The environmental fields and/or more complex spins change the probability of finding various ground states even if they are members of disconnected components in the simple formulation. So it also depends on the fidelity of the modeling as to whether systems are decomposable into subsystems or not. From: Friam [mailto:friam-boun...@redfish.com] On Behalf Of Stephen Guerin Sent: Saturday, May 27, 2017 7:08 PM To: The Friday Morning Applied Complexity Coffee Group <friam@redfish.com> Subject: Re: [FRIAM] Any non-biological complex systems? Yes, and systems can have subsystems. In my comment to Glen, my point was that a phase space is a description of a single system. -S _______________________________________________________________________ stephen.gue...@simtable.com<mailto:stephen.gue...@simtable.com> CEO, Simtable http://www.simtable.com<http://www.simtable.com/> 1600 Lena St #D1, Santa Fe, NM 87505 office: (505)995-0206 mobile: (505)577-5828 twitter: @simtable On Sat, May 27, 2017 at 7:07 PM, Frank Wimberly <wimber...@gmail.com<mailto:wimber...@gmail.com>> wrote: For what it’s worth, a linear space can have a subspace that is a linear space. Both the larger and smaller spaces are linear spaces. Of course “linear space” is much more precisely defined than “system”. Frank Frank C. Wimberly 140 Calle Ojo Feliz Santa Fe, NM 87505 wimber...@gmail.com<mailto:wimber...@gmail.com> wimbe...@cal.berkeley.edu<mailto:wimbe...@cal.berkeley.edu> Phone: (505) 995-8715<tel:(505)%20995-8715> Cell: (505) 670-9918<tel:(505)%20670-9918> From: Friam [mailto:friam-boun...@redfish.com<mailto:friam-boun...@redfish.com>] On Behalf Of Stephen Guerin Sent: Friday, May 26, 2017 6:40 PM To: The Friday Morning Applied Complexity Coffee Group Subject: Re: [FRIAM] Any non-biological complex systems? Glen writes: Not quite. If these systems merely contain subsystems capable of exhibiting complexity, then those 3 you listed are not complex systems. They are "subsystems capable of exhibiting complexity". So, no. They are not complex systems in isolation. Russ' question, I think, targets naturally occurring, whole complex systems. We disagree on the use of systems and subsystems in the context of phase space then. To me, there is one system and that system has a phase space - There are not multiple subsystems in the phase space. And as there are multiple use of phase space I mean it in this sense: https://en.wikipedia.org/wiki/Phase_space The phase space can also refer to the space that is parametrized by the macroscopic states of the system, such as pressure, temperature, etc. For instance, one may view the pressure-volume diagram or entropy-temperature diagrams as describing part of this phase space. A point in this phase space is correspondingly called a macrostate. There may easily be more than one microstate with the same macrostate. For example, for a fixed temperature, the system could have many dynamic configurations at the microscopic level. When used in this sense, a phase is a region of phase space where the system in question is in, for example, the liquid<https://en.wikipedia.org/wiki/Liquid> phase, or solid<https://en.wikipedia.org/wiki/Solid> phase, etc. _______________________________________________________________________ stephen.gue...@simtable.com<mailto:stephen.gue...@simtable.com> CEO, Simtable http://www.simtable.com<http://www.simtable.com/> 1600 Lena St #D1, Santa Fe, NM 87505 office: (505)995-0206<tel:(505)%20995-0206> mobile: (505)577-5828<tel:(505)%20577-5828> twitter: @simtable On Fri, May 26, 2017 at 6:08 PM, glen ☣ <geprope...@gmail.com<mailto:geprope...@gmail.com>> wrote: On 05/26/2017 04:54 PM, Stephen Guerin wrote: > I am listening to Russ. I do think he's defining a sub-class of complex > systems (eg living systems). I would like to keep the definition of > "complex systems" broader than that though. OK. But I don't think he's necessarily _asserting_ that only living systems are complex systems. He's just asking the question and engaging in a discussion wherein we might be able to refine his sub-category so that it includes physical systems. > I understand the subtle distinction your trying to make. I would say the > full phase space of a *complex system* has narrow critical regimes in their > behavior (phase) space where *complex behavior* is observed as the control > parameters are swept through the phase transition. In the critical regime > we see complex behavior like sensitivity to initial conditions, critical > slowing down, critical fluctuations, power law statistics, long-range > correlations, etc. On either side of the phase transition (eg sub-critical > and super-critical) regimes, these statistics and behaviors are not present. > > That said, while the critical regime may be narrow in phase space many of > these system "self-tune" to the critical point but that's another thread. > > Agreed? Not quite. If these systems merely contain subsystems capable of exhibiting complexity, then those 3 you listed are not complex systems. They are "subsystems capable of exhibiting complexity". So, no. They are not complex systems in isolation. Russ' question, I think, targets naturally occurring, whole complex systems. Now, if we add the experimental apparatus that, eg, maintains a ZB reaction for a long time, then that _whole_ system can be called a complex system. But there's significant meat to the controlling subsystem ... and we biological creatures instantiated it. The case is the same with, say, glycolysys. All you need do is identify the circumstances where those three processes (ferromag, benard cells, BZ reactions) occur in nature and then we might be able to identify the systems in which they sit. Then we can test them against whatever predicate we want. -- ☣ glen ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
