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Well, of course, there are. For example, the electric field has such a characteristic – potential, and the potential of the point charge field depends on the distance to the charge as 1/r (you need to multiply by some coefficients, but the dependence is inversely proportional). However, in order to correctly determine the potential, it is necessary to agree at which point it is zero. For a point charge, the potential is assumed to be zero precisely at infinity.
Take a point charge, build a beam from it in any direction, and place a conducting wire in this beam that does not come into contact with the charge itself. If a voltmeter terminal is attached to one end of it, and the second one is moved away from the first, then the voltage will decrease according to the law 1/r, again up to multiplication by a constant and adding a constant.
If the word “potential” scares you for some reason, then take the function 1/x^2. Get the law according to which the force of gravitational attraction decreases with the removal of bodies.
As an introduction, it is worth saying that it is not physical processes that adapt to mathematical equations, but equations and functions that describe existing physical processes. At the same time, mathematics is only a language that partially or incompletely describes an existing process. Therefore, there are no real physical processes that correspond exactly to y = 1/x.
If we talk about a physical model, then such a process can be invented. Take, for example, a material point moving by inertia, and start applying a force against it (that is, slowing down the movement) acting on the point in proportion to the mass, but at the same time weakening the action from time to time in proportion to its square, that is, F ~ -m/(t^2). �Then, relative to the speed of movement, you will get the differential equation dv(t) = – dt / (t^2), solving which you will get that v = 1/t, that is, the speed of the point decreases with time, but never becomes zero
You can give such a clear example from life:
Let y be the cake you have, and x be the number of friends you want to share it with (and give everyone the same piece).
It is clear that the more guests you have, the less each of them will get.
Well, what if, for example, you decide to share your little cake with the whole city, which, say, has a million inhabitants? (we direct x to infinity) Obviously, every citizen will get almost nothing, that is, 0 grams of cake. Formally, it may be a couple of crumbs, but we can absolutely legally round to zero.