# Some Consequences of the Thermodynamic Cost of System Identification

## TL;DR

This paper explores how the thermodynamic costs and limitations of finite observations affect the process of system identification, revealing that such identification is inherently approximate and linked to quantum inequality violations.

## Contribution

It demonstrates that finite thermodynamic resources impose fundamental constraints on system identification, leading to natural emergence of quantum inequality violations.

## Key findings

- System identification is inherently approximate due to thermodynamic costs.
- Violations of Leggett--Garg and Bell inequalities arise from identification constraints.
- Finite observations limit the precision of system identification in physics.

## Abstract

The concept of a ``system'' is foundational to physics, but the question of how observers identify systems is seldom addressed. Classical thermodynamics restricts observers to finite, finite-resolution observations with which to identify the systems on which ``pointer state'' measurements are to be made. It is shown that system identification is at best approximate, even in a finite world, and that violations of the Leggett--Garg and Bell/CHSH (Clauser-Horne-Shimony-Holt) inequalities emerge naturally as requirements for successful system identification.