tag:blogger.com,1999:blog-6837159629100463303.post4778901539375282995..comments2021-07-22T00:29:53.205-07:00Comments on Information Transfer Economics: On the use of hypotheses: or, what do you get when you assume non-ergodicity?Jason Smithhttp://www.blogger.com/profile/12680061127040420047noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-6837159629100463303.post-12545639702944282242015-05-12T08:56:07.857-07:002015-05-12T08:56:07.857-07:00There is also a possibility of "symmetry brea...There is also a possibility of "symmetry breaking" ... that is very much related to the coordination that happens during a market panic. Normally everyone engages in transactions and since there are at least two sides of each deal, the market moves tend to cancel each other out (on average).<br /><br />During a panic both sides of each deal are pessimistic -- their behavior becomes coordinated by news. The randomness is replaced by a particular direction to prices (typically down), entropy falls and the original symmetry (the two sides of the deal) is "broken".<br /><br /><a href="http://informationtransfereconomics.blogspot.com/2014/10/coordination-costs-money-causes.html" rel="nofollow">http://informationtransfereconomics.blogspot.com/2014/10/coordination-costs-money-causes.html</a><br /><br />The example at the wikipedia article uses a magnet -- the original disordered state has a rotational symmetry (iron atom spins aren't lined up, so they don't point in any particular direction on average), but it is possible for them to move into an aligned state. That aligned state (with a macroscopic direction to the magnetic moment vector) breaks the rotational symmetry of the disordered state -- that symmetry breaking breaks the ergodicity as well.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-8619140980490971812015-05-11T03:53:19.902-07:002015-05-11T03:53:19.902-07:00Oh, I see. I don't think you can get much if y...Oh, I see. I don't think you can get much if your system doesn't preserve a probability (or without assuming some sort of stationarity condition).<br /><br />The Wikipedia article on the ergodic hypothesis says that certain physical systems satisfy the hypothesis but some don't. I don't understand the article very well because I was taught the subject from a mathematical (not physical) point of view. I don't know if there are applications to economics but it wouldn't surprise me if this is the case.<br /><br />http://en.wikipedia.org/wiki/Ergodic_hypothesisMnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-22756514689498580102015-05-10T13:26:25.849-07:002015-05-10T13:26:25.849-07:00That's an interesting article -- all measure p...That's an interesting article -- all measure preserving dynamic systems can be decomposed into ergodic components.<br /><br />I bet some of the complex and chaotic systems people want to use for economics are measure preserving in this sense -- a rude awakening for them!<br /><br />I was using non-ergodic in its most general sense ... which may not be measure preserving. Bits of phase space disappear forever or probability distributions may collapse to delta functions. That kind of stuff.<br /><br />But I didn't know ergodic systems were like the prime numbers of dynamic systems.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-5147217676234624312015-05-10T12:31:53.500-07:002015-05-10T12:31:53.500-07:00This is the decomposition I am talking about:
htt...This is the decomposition I am talking about:<br /><br />https://joelmoreira.wordpress.com/2013/09/20/ergodic-decomposition/<br /><br />But perhaps we mean different things by ergodicity.Mnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-86233183436169820832015-05-10T11:45:05.050-07:002015-05-10T11:45:05.050-07:00I think ergodic systems can be broken into differe...I think ergodic systems can be broken into different ergodic pieces; however, I don't think there is any general result for a non-ergodic system, but maybe I am just unaware of it.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-18130221723820964392015-05-10T00:45:46.840-07:002015-05-10T00:45:46.840-07:00Well, a non-ergodic system can be decomposed to er...Well, a non-ergodic system can be decomposed to ergodic systems, right? Doesn't that allow us to get something even without assuming ergodicity?Mnoreply@blogger.com