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Of course there is no foundational medium to become equalized in General Relativity Theory, but in GR the approach of heat death is the trend toward the elimination of energy differentials and the related elimination of any ability for life to exist or of any available energy to do work in the universe on a grand scale. You can immediately see the distinction between the GR heat death and the equalization of energy density at the micro limit in my model simply by realizing that I am talking about the infinitesimal end of the size scale, i.e. in the tiniest space, patches of medium at the point by point intersection of intersecting wave fronts. Never have I given any indication that the grand scale heat death is possible in my model, and I will confirm that again, the universe in my model is infinite and filled infinitely with the foundational medium and every tiniest patch of medium is always being intersected by waves of varying pressure from all directions. That is until energy density equalization occurs in the tiniest of all possible patches of space and accumulates behind any given advancing wave front for a short duration.
"At the micro level the limit is called "equalized energy density", i.e. when all of the tiny intersecting and overlapping pressure zones that are expanding into a given infinitesimal patch of medium in space are of equal pressure, that patch of medium is equalized. Without a pressure differential there is no high density spot at the point of intersection of those convergences and therefore there is no spherical outflowing wave energy from a high density spot, meaning that the wave front has advanced past that point as it traverses the medium. Even though the medium fills that space and has a positive pressure relative to empty space, there is no further equalization occurring at that point in space and time; equalized energy density has occurred within that patch of medium.
In my model at the macro level, big bangs happen all the time across the arena landscape of the greater universe, while at the micro level, equalized patches of medium occur all the time as a result of the advancing wave front of a pressure wave. Their appearance indicates that equalization of the differential between the advancing wave front and the pressure of the medium it is intruding into has occurred and the pressure behind the advancing wave front is equalized to the net combined pressure of the converging pressure waves. The accumulation of tiny equalized pressure zones merges in behind the advancing front to create the equalized condition between the two waves after they converge. That zone of equalized energy density exists until it is interrupted by converging with another pressure wave."