the relationship between a homogeneous system, and heterogenous system, which are two contradictory states of a system, are equivalent through transformations occurring over time, making it possible to connect them through a kind of Noether's Theorm, and isomorphism. Just imagine an all white (homogenous) 10x10 grid, and a random (heterogenous)10x10 grid. To go from one state to the other, requires a transformation or a rule that the pixels in the grid follow to get to the next state. Since any state can potentially take only 1 transformation (a transform that requires 100 simultaneous operations), then it is one such hard proof that there is a universality between all the possible permutations of states. Time becomes the variable, rather then the system. The system is "the same" just being transformed over time. You can then generically classify that relationship as "system evolution" Another thing : Universal Heat Death is fundamentally flawed for the following reason. There exists no system that can actually be at an equilibrium that doesn't exhibit a structured predictable pattern, meaning there will always exist information, and the question is at what scale can that information actually be utilized, by an observer that is comparable to the scale of the system. Let's just assume that the universe were made of 0's and 1's. a truly random string of 0's and 1's : 00111101101000101 obviously has some structure. There are a series of predictable patterns (1111, 000, 101) meaning this random string of numbers is not devoid of information. it ALWAYS has information. If you take every computational bit to be unique (DEFKMABLGHJIN etc...), then the information content is not only always there, but it is maximal at all times...because in a random string of symbols, there are no symbols it can relate to based on repeatability, then what gives context to what symbols mean, are what symbols they are next to. In that above sequence, "K" means nothing to the letter "D" until "D" recognizes that K is next to the letters F and M... So when D asks a question about F, he knows that K is next to F. Based on the connection between each unique element, then observers of this universe will interpret it exactly as that, based on it's relationship structure in this case how it's orientation in space relative to one another...K is next to M, M is next to A and so on...and this means something for observers in the universe, just at a scale that encompasses the entire universe. It's likely that, the universe is like the second case, where all computational elements are unique, like in the wolfram model of physics. In such a universe, "heat death" doesn't really have a meaning because the universe is always at a maximal state of information, and in some sense you can't interfere with that. It's like...You can move letter B next to letter E, so that the new sequence is DBEFKMALGHJIN...the sequence still remains maximally random...but the relationship that B has is changed (It's now next to D and E instead of A and L), and this matters for the observers in this system. In other words there is ALWAYS a conservation law of the information, energy and whatever at any given configuration of this universe and its the observers in that universe that are deciding exactly what the "state" of the universe is. **In both scenarios Heat Death does not truly exist in any information theoretic sense. Folks assume that equilibrium, where the universe is maximally homogeneous at all scales is the same as heat death, but this is not true... like shown above, maximal randomness always has by just virtue of statics, patterns...and in the opposing case where the universe is made of unique elements, then it is ALWAYS at maximal information content which doesn't undergo Heat Death.**