Brownian motion: Difference between revisions

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{{drop|Y|ou will hear}} it said that the surface of the proverbial “nice hot cup of tea” tends to stillness only through the awesome force of [[entropy]]. The particles ricocheting this way and that in the liquid, colliding chaotically, and you only do not notice them because of the vast ''improbability'' that enough particles all happen move the same way at once.
{{drop|Y|ou will hear}} it said that the surface of the proverbial “nice hot cup of tea” tends to stillness only through the awesome force of [[entropy]]. The particles ricocheting this way and that in the liquid, colliding chaotically, and you only do not notice them because of the vast ''improbability'' that enough particles all happen move the same way at once.


The state of a system is “ordered” when only a few arrangements could produce that state. It is in a state of chaos when many arrangements could produce the same state. The larger systems get the more ways there are for them be chaotic so, if left alone, systems tend to disorder. That is, ''entropy''.
A system appears “ordered” when only a few arrangements, out of many, could produce a recognisable state. It is in a state of chaos when many arrangements could produce the same state. Twenty blocks stacked on top of each other: ordered. Twenty blocks scattered on the floor: chaotic. There are countless ways of scattering blocks across the floor; only a few ways of stacking them. The larger systems get the more ways there are for them be chaotic so, if left alone, systems tend to disorder. That is, ''entropy''.


In this sense, entropy is just a statement of basic probability: the larger the number of particles there are, the more scope there is for chaos.
In this sense, entropy is just a statement of basic probability: the larger the number of particles there are, the more scope there is for chaos.
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But this kind of interdependence reinforces normal behaviour. When “non-autonomous” events interact with each the interactions are also random, and  tend to cancel each other out.
But this kind of interdependence reinforces normal behaviour. When “non-autonomous” events interact with each the interactions are also random, and  tend to cancel each other out.


''Inter''dependent events — at least those propelled by ''autonomous'' actors ''don’t'' always cancel each other out. Autonomous agents can anticipate and avoid collisions (what this happening at King’s cross Station at rush hour). They can turn and run in the same direction as oncoming traffic. Tea molecules can’t jump out of the tea-cup at the same time. Participants in a securities market can and, from time to time, do.
''Inter''dependent events — at least those propelled by ''autonomous'' actors ''don’t'' always cancel each other out. Autonomous agents can anticipate and avoid collisions (what this happening at King’s Cross Station at rush hour). They can turn and run in the same direction as oncoming traffic. Tea molecules can’t jump out of the tea-cup at the same time. Participants in a securities market can and, from time to time, do.


{{Sa}}
{{Sa}}