Prestatability in the Macroscopic Limit
Abstract
We examine whether the variables required for a future macroscopic description of a given physical system can themselves be stated in advance. Representing macroscopic descriptions as coarse-grainings of a fixed microscopic phase space, we distinguish formal prestatability, concerning the existence of an effective complete vocabulary of admissible macroscopic distinctions, from dynamical prestatability, concerning whether the future relevance of those distinctions is decidable. Both obstructions disappear for finite microscopic state spaces. In the infinite limit, exhaustive formal prestatability can fail, while a restricted predictive architecture may remain formally pre-statable. We construct such an architecture and show that, under universal dynamics, the future relevance of a candidate variable is equivalent to the halting problem. Thus a fixed microscopic phase space can support macroscopic descriptions whose future variables are not fully pre-statable.
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BibTeX
@misc{palessandro2026prestatability,
title = {{Prestatability in the Macroscopic Limit}},
author = {Andrea Palessandro},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.09989},
eprint = {2611.09989},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.09989},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Prestatability in the Macroscopic Limit
AU - Andrea Palessandro
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.09989
UR - https://arxiv.org/abs/2611.09989
AB - We examine whether the variables required for a future macroscopic description of a given physical system can themselves be stated in advance. Representing macroscopic descriptions as coarse-grainings of a fixed microscopic phase space, we distinguish formal prestatability, concerning the existence of an effective complete vocabulary of admissible macroscopic distinctions, from dynamical prestatability, concerning whether the future relevance of those distinctions is decidable. Both obstructions disappear for finite microscopic state spaces. In the infinite limit, exhaustive formal prestatability can fail, while a restricted predictive architecture may remain formally pre-statable. We construct such an architecture and show that, under universal dynamics, the future relevance of a candidate variable is equivalent to the halting problem. Thus a fixed microscopic phase space can support macroscopic descriptions whose future variables are not fully pre-statable.
ER -