tag:blogger.com,1999:blog-6837159629100463303.post8633377521433762774..comments2019-10-22T10:42:44.561-07:00Comments on Information Transfer Economics: Causal entropic forces as economic forcesJason Smithhttp://www.blogger.com/profile/12680061127040420047noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6837159629100463303.post-91640578021411926732016-09-02T18:43:02.711-07:002016-09-02T18:43:02.711-07:00Aren't these only transitory and apparent? As ...<i>Aren't these only transitory and apparent? As the system settles into entropic equilibrium will not these apparent gradients disappear?</i><br /><br />The entropy gradients are in configuration space, so they "always exist". The system just experiences the entropic force if it finds itself in a part of configuration space where there is a gradient (e.g. any non-uniform density distribution in the diffusion case). The system will settle into equilibrium eventually (no need to call it an 'entropic' equilibrium -- thermodynamic equilibrium is where entropy is maximized); that equilibrium is a part of configuration space with no gradient (i.e. a local maximum).<br /><br /><i>Exactly, so what's new?</i><br /><br />The part where the causal horizon is not at infinity (t < ∞).<br /><br />Not sure why you put the "exactly" there. You can't simultaneously think the definition of causal entropy is invalid and that it somehow has a valid limit. And if you understood the sentence that you quoted (a prerequisite for the "exactly"), then you wouldn't have asked the question after it because you would have known that the part that is new is where t < ∞.<br />Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-16217053157882828362016-09-02T15:01:32.049-07:002016-09-02T15:01:32.049-07:00" The force arises from entropy gradients......." The force arises from entropy gradients...."<br /><br />Aren't these only transitory and apparent? As the system settles into entropic equilibrium will not these apparent gradients disappear?<br /><br /><br /><br />"Considering only causal configurations and calling that causal entropy is fine as long as you label it as such."<br /><br />So giving it a name renders it valid?<br /><br />"Additionally in the long time limit the two definitions coincide (e.g. as time goes to infinity the causal volume of position states is the entire set of accessible position states)."<br /><br />Exactly, so what's new?<br /><br /> <br /><br /><br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-46725936069432765492016-09-02T14:47:59.010-07:002016-09-02T14:47:59.010-07:00What is the source of causal entropic force?
Much...<i>What is the source of causal entropic force?</i><br /><br />Much like an entropic force, there is no microscopic source. The force arises from entropy gradients (e.g. the "source" of the entropic force of <a href="https://en.wikipedia.org/wiki/Diffusion" rel="nofollow">diffusion</a> is the non-uniform occupation of position states in the container).<br /><br /><i>Doesn't the notion of a causal force entirely contradict the notion of entropy?</i><br /><br />Which aspect of entropy does it contradict? Entropy is a measure of the number of possible configurations of a system. Considering only causal configurations and calling that causal entropy is fine as long as you label it as such. Additionally in the long time limit the two definitions coincide (e.g. as time goes to infinity the causal volume of position states is the entire set of accessible position states).<br /><br />Essentially lim t→∞ of F_t = T ∇ S_t is the entropic force formula F = T ∇ S.<br /><br />Also you might consider that as the paper was published in <i>Physical Review Letters</i> one of the reviewers might have noticed if there was an egregious problem :)Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-34489329527066482242016-09-02T14:06:57.505-07:002016-09-02T14:06:57.505-07:00What is the source of causal entropic force?
Does...What is the source of causal entropic force?<br /><br />Doesn't the notion of a causal force entirely contradict the notion of entropy?Anonymousnoreply@blogger.com