Not sure if this is helpful, and sorry if this is old news to you, but instead of saying information is “wiped out”, I think there’s a complementary perspective in which information is preserved (cf. Liouville’s theorem in classical mechanics, or unitarity in QM), but information very often has the tendency to transform from “useful / actionable information” to “useless information”. For example:
The following information is useful / actionable: “At time t=17.123 seconds, every air molecule in the container will be in the left half”. Why is it actionable? Because I can wait until t=17.123 seconds and quickly slip a divider into the container to separate the left and right halves, attach it to a piston, and extract negentropy from the pressure.
The following information is useless: “The 17th decimal place of the velocity of particle 79 is ‘4’, and the 19th decimal place of the velocity of particle 857 is ‘6’, and […1020 more statements like that]”. I can know that information with 100% certainty, yet there’s no possible action I can take that will extract negentropy using that knowledge.
You can come up with fun edge cases of information that might or might not be “useful” depending on what tools you have on hand, etc.
There’s a nice description here of how, if I know that a system is in a coherent blob of phase space at time 0, then my knowledge at much later times is “the system is in a particular subregion of phase space that looks like ever-finer filamentary threads spread all around phase space”—and that tends to be useless information.
Anyway, for your purposes, I guess you can say “What does the total phase space (≈ high-dimensional possibility space) look like? Given information of the form ‘the system is in X part of phase space’, what are the values of X such that this information be plausibly useful / actionable / decision-relevant? Given that I observe / know some constraint at time t=0, the information I have at time t=5 seconds will be ‘the system is in a region that looks like a filamentary mess spreading ever-finer tendrils around phase space’—but what are the constraints on that filamentary mess?” Maybe asking such questions would be fruitful brainstorming, if you haven’t already. :)
In this story, the topological mixing of the phase space (i.e. ever thinner filaments of phase space volume filling all space) and a low resolution mesh on the phase space (only a few low order bits) mean that there will be filaments in every part of the mesh. Hence your system could now be anywhere in the mesh, and is “unpredictable”.
Anyway, I believe there are asynchronous theories of thermodynamics, but the field hasn’t settled on which one is right. These three papers [1][2][3] describe asynchronous formulations of relativstic thermodynamics, and I first read about the topic on SEP, but I can’t find the article anymore. It was quite good. This paper [4] gives an overview of various approaches to relativistic thermodynamics, but it is quite old and I don’t know what the state of the art is like. Or really what the various viewpoints are. It has been a while since I looked at this.
Not sure if this is helpful, and sorry if this is old news to you, but instead of saying information is “wiped out”, I think there’s a complementary perspective in which information is preserved (cf. Liouville’s theorem in classical mechanics, or unitarity in QM), but information very often has the tendency to transform from “useful / actionable information” to “useless information”. For example:
The following information is useful / actionable: “At time t=17.123 seconds, every air molecule in the container will be in the left half”. Why is it actionable? Because I can wait until t=17.123 seconds and quickly slip a divider into the container to separate the left and right halves, attach it to a piston, and extract negentropy from the pressure.
The following information is useless: “The 17th decimal place of the velocity of particle 79 is ‘4’, and the 19th decimal place of the velocity of particle 857 is ‘6’, and […1020 more statements like that]”. I can know that information with 100% certainty, yet there’s no possible action I can take that will extract negentropy using that knowledge.
You can come up with fun edge cases of information that might or might not be “useful” depending on what tools you have on hand, etc.
There’s a nice description here of how, if I know that a system is in a coherent blob of phase space at time 0, then my knowledge at much later times is “the system is in a particular subregion of phase space that looks like ever-finer filamentary threads spread all around phase space”—and that tends to be useless information.
Anyway, for your purposes, I guess you can say “What does the total phase space (≈ high-dimensional possibility space) look like? Given information of the form ‘the system is in X part of phase space’, what are the values of X such that this information be plausibly useful / actionable / decision-relevant? Given that I observe / know some constraint at time t=0, the information I have at time t=5 seconds will be ‘the system is in a region that looks like a filamentary mess spreading ever-finer tendrils around phase space’—but what are the constraints on that filamentary mess?” Maybe asking such questions would be fruitful brainstorming, if you haven’t already. :)
In this story, the topological mixing of the phase space (i.e. ever thinner filaments of phase space volume filling all space) and a low resolution mesh on the phase space (only a few low order bits) mean that there will be filaments in every part of the mesh. Hence your system could now be anywhere in the mesh, and is “unpredictable”.
Anyway, I believe there are asynchronous theories of thermodynamics, but the field hasn’t settled on which one is right. These three papers [1][2][3] describe asynchronous formulations of relativstic thermodynamics, and I first read about the topic on SEP, but I can’t find the article anymore. It was quite good. This paper [4] gives an overview of various approaches to relativistic thermodynamics, but it is quite old and I don’t know what the state of the art is like. Or really what the various viewpoints are. It has been a while since I looked at this.
[1] A. Gamba, “Physical quantities in different reference systems according to relativity,” American Journal of Physics, vol. 35, pp. 83–89, 1967.
[2] G. Cavalleri and G. Salgarelli, “Revision of the relativistic dynamics with variable rest mass and application to relativistic thermodynamics,” Il Nuovo Cimento A, vol. 62, no. 3, pp. 722–754, 1969.
[3]Ø. Grøn, “The asynchronous formulation of relativistic statics and thermodynamics,” Nuovo Cimento, vol. 17, pp. 141–165, 1973.
[4] https://doi.org/10.1119/1.1976295