Historical Side Information and the Reversal of Open-System Dynamics
- 1Department of Chemistry, University of Pavia, V.le Taramelli 13, Pavia, Italy, I27100
Abstract
Microscopic reversibility guarantees the existence of a time-reversed trajectory for a globally reversible dynamical system, but does not by itself guarantee that a later controller possesses the physical information required to identify and implement that trajectory. For an open system, distinctions between different microscopic histories may become encoded in environmental correlations whose physical carriers disperse, degrade, or become inaccessible, even though the corresponding information remains present in the global state. We formulate this distinction in terms of the physically accessible state of the controller and introduce a task-dependent measure of historical reversal information: the additional physically realizable information required to achieve a prescribed reversal accuracy. For continuous systems, a local Gaussian model yields a rate–distortion lower benchmark whose high-resolution behavior separates a geometrical contribution from a dynamical amplification term. For chaotic dynamics, the latter can acquire a Pesin-type form proportional to the relevant positive Lyapunov exponents. We then distinguish practical loss of accessibility from causal inaccessibility. When carriers of reversal-relevant information cross a causal horizon, subsequent information backflow to the controller is excluded. Finally, we consider a finite physical memory and show, in a minimal model, that memory saturation followed by logical erasure links the loss of accessible historical distinctions to Landauer entropy production. If the corresponding erasure heat is transferred across a horizon, this yields a lower bound on the associated horizon-entropy and area increase. The resulting framework separates global information preservation from local physical recoverability and shows how openness, dynamical instability, finite record capacity, and causal structure can jointly limit the reversal of a particular realized history without violating microscopic reversibility.
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BibTeX
@misc{ghigna2026historical,
title = {{Historical Side Information and the Reversal of Open-System Dynamics}},
author = {Paolo Ghigna},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15009100/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009100/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Historical Side Information and the Reversal of Open-System Dynamics
AU - Paolo Ghigna
PY - 2026
DA - 2026/09/20
PB - ChemRxiv
DO - 10.26434/chemrxiv.15009100/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009100/v1
AB - Microscopic reversibility guarantees the existence of a time-reversed trajectory for a globally reversible dynamical system, but does not by itself guarantee that a later controller possesses the physical information required to identify and implement that trajectory. For an open system, distinctions between different microscopic histories may become encoded in environmental correlations whose physical carriers disperse, degrade, or become inaccessible, even though the corresponding information remains present in the global state. We formulate this distinction in terms of the physically accessible state of the controller and introduce a task-dependent measure of historical reversal information: the additional physically realizable information required to achieve a prescribed reversal accuracy. For continuous systems, a local Gaussian model yields a rate–distortion lower benchmark whose high-resolution behavior separates a geometrical contribution from a dynamical amplification term. For chaotic dynamics, the latter can acquire a Pesin-type form proportional to the relevant positive Lyapunov exponents. We then distinguish practical loss of accessibility from causal inaccessibility. When carriers of reversal-relevant information cross a causal horizon, subsequent information backflow to the controller is excluded. Finally, we consider a finite physical memory and show, in a minimal model, that memory saturation followed by logical erasure links the loss of accessible historical distinctions to Landauer entropy production. If the corresponding erasure heat is transferred across a horizon, this yields a lower bound on the associated horizon-entropy and area increase. The resulting framework separates global information preservation from local physical recoverability and shows how openness, dynamical instability, finite record capacity, and causal structure can jointly limit the reversal of a particular realized history without violating microscopic reversibility.
ER -