The work cost of answering in real time
In plain wordsA device that must answer each request before the next arrives pays a least work per run fixed by one entropy-plus-energy quantity, and order alone can cost work: a process free when its outputs may wait can cost work when they may not, even classically.
The result
As the paper states it, in briefThe work law for devices that must answer each request before the next arrives while remembering what came before.
Questionson the index
- Partly answered Do thermal operations reach the thermodynamic capacity of a channel that is not time-covariant? posed by others
How this was checked
- Blind checks
- Every result passed a blind refutation-first check
- Machine checks
- Machine checks in Python
- In Lean
- Finite and algebraic cores in Lean with Mathlib.
- Lean
- Selected parts.
- Peer review
- Not yet.
The verification label is the one shared by the four companion papers, given in full on The price of time order.
Every check here is internal. How we check results.
Novelty and credit
- Novelty
- Extends named prior work: it settles, for real-time processes, the analogue of a question of Faist, Berta and Brandão, and its free-process theorem is a robust form of the criterion of Lie, Son, Boes, Ng and Wilming. For channels it reduces to Only quantum channels save work by waiting.
Versionsthree, each with its own DOI
| Version | Date | DOI | Notes |
|---|---|---|---|
| 1.0.2 | 10.5281/zenodo.23323045 | PDF hosted here. | |
| 1.0.1 | 10.5281/zenodo.23310737 | ||
| 1.0.0 | 10.5281/zenodo.23310629 |
Paper, code and links
papers/real-time-v1.0.2.pdf, version 1.0.2, 747,995 bytes.SHA-256 c42136a7a1b1e7bba464967c51967609a857411e8682ab1bbda0b8f96f3dceb1
- DOI
10.5281/zenodo.23323045; all versions 10.5281/zenodo.23310628
Corrections
- The four thermodynamics papers of 11 October cited Thompson et al. with a DOI that did not resolve. Version 1.0.2 of each paper gives the correct DOI, 10.1103/dryx-l5rt.
All corrections, and what counts as one.
Cite
@misc{douglas2026realtime,
author = {Douglas, Seth and Mghirbi, Nidhal},
title = {The work cost of answering in real time},
year = {2026},
version = {1.0.2},
doi = {10.5281/zenodo.23323045},
url = {https://doi.org/10.5281/zenodo.23323045}
}