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.
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