Everyday entropy: equilibrium

Degrees of freedom

At equilibrium, where entropy is at its maximum, the increase in energy is equal to the increase in available space.  But, for an individual particle, ontologically, there is no uncertainty and it’s location and relative momentum (not its rest mass) are meaningless.  At any given moment, its internal entropy is zero because it has no configuration.  The energy, momentum and uncertainty, according to the Copenhagen interpretation, arise from the particle’s interactions with other particles and our knowledge about those interactions.

To understand why this relationship may be significant in our world, even though we never experience absolute zero, let us imagine a gas particle in free space.  It may have been in a cloud at a million degrees before it escaped, but now it is interacting with nothing.  Within its frame, it has no momentum.  If we put a box around it, the box would have no temperature, even though the particle hasn’t released any energy since leaving its cloud.  Now let’s imagine that particle back in its cloud.  At any given time, it is as free as it was in open space.  Only at moments when it interacts with other particles does its energy become relevant, when it either emits or receives force carriers.  These transmissions may be virtually continuous, but they are quantised, which means they occur one at a time, in steps, and not as a continuous blend of interactions.  Each emission and absorption is instantaneous and separated in time from all other emissions and absorptions.  The point here is not that a particle lives at absolute zero, but that its energy level is an average of the force emissions and absorptions in its interactions, rather than an inherent quality of the particle itself.  Whether one particle gains or gives a virtual photon from or to another depends on your frame of reference.  And this is where the virtual force carriers that mediate interactions between physical particles differs from the “real” photons of light emissions, which are absolute and have no frame.
The point is that for a massive particle, space and momentum offer equal freedom.  The equivalence of the freedom of energy and space in the physical universe may allow for the fluid transitions between volume and force.  This is not to say that physical and informational entropy are unrelated, only that their relationship is asymmetrical for a number of reasons that may not be trivial.  The two entropies may be interwoven, but they cannot be unified into a single theory of universal entropy because one is ontological and the other epistemological, and they have different shapes and functions.

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