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While I'm not proud of this coming sentence, in physics a lot of different things turn out to be roughly the same thing. For example, the flow of electricity is very much like the flow of water, and so voltage closely corresponds to pressure, current closely corresponds to flow rate.

It occurs to me that there seems to be such a similarity between temperature and pressure. Both naturally equalize in an open system. Both fight harder and harder the more extreme the gradients, the temperature manifestation of which is Newton's Law of Cooling, and the pressure manifestation of which is the explosion that results when you puncture a propane can, as opposed to the much smaller explosion resulting from puncturing a whipped cream canister. Moreover, the two are even caused by the same set of factors, which is why we have laws relating the two. But are they duals of each other? Is there a Newton's Law of Depressurization, and so on?

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  • $\begingroup$ But they are both just following a more fundamental law of conservation of energy and the thermodynamic laws.......and yeah, your first sentence, whoa..........: ) maybe using the word analogous in it somewhere might have been better. Best of luck with your question though. $\endgroup$ – user108787 Nov 24 '16 at 19:14
  • $\begingroup$ The ideal gas law says they're proportional to each other... $\endgroup$ – Kyle Kanos Nov 24 '16 at 19:23
  • $\begingroup$ The subject you want to study is thermodynamics, though I prefer to tackle in with a lot of statistics so you might look for a treatment of "thermal physics". $\endgroup$ – dmckee Nov 24 '16 at 20:14
  • $\begingroup$ I thought about your point, and I could not think of any physical argument to refute it. But I also could not think of any use it could put to, unlike for example, vectors versus forms. $\endgroup$ – user108787 Nov 25 '16 at 0:43
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I don't know about duality... but yes, pressure of a container with a leak would decrease with a negative exponential, as does temperature in Newton's cooling, as does a discharging capacitor, or radioactivity. All solutions to the same differential equation: the rate of decrease is proportional of what is there.

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  • $\begingroup$ So you're saying that these shared properties are not qualities of temperature and pressure specifically, but a far larger set of quantities? There's a bigger picture? $\endgroup$ – TheEnvironmentalist Nov 27 '16 at 17:11

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