Certifying Hidden Dissipation from Observed Current Fluctuations
Abstract
A single-molecule experiment on a driven enzyme or motor resolves only a few of the transitions the machine makes, yet one would like to know how much free energy it dissipates in total, including on the steps that stay hidden. The mean and the fluctuations of the currents on the watched transitions are shown to certify this hidden dissipation, with no knowledge of the transition rates and no access to the hidden transitions: when the watched transitions span the cycles of the network, the observed-current covariance recovers the full density-contracted quadratic current geometry, including the contribution of transitions that are never seen. The mechanism is that fluctuations are set by the dynamical activity, or traffic, the symmetric partner of the current. Contracting the large-deviation cost of empirical currents over density fluctuations identifies the observed-current covariance with a traffic-weighted metric, and turns partial observation into a minimum-energy completion problem over the unseen cycles, whose solution is the certified hidden cost. Existing current-fluctuation uncertainty relations bound dissipation from chosen currents but do not say when partial observation fixes the hidden contribution; the cycle-observability condition derived here does. The statements concern long-time means and fluctuations; finite-time estimates require separate error control.
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BibTeX
@misc{roman2026certifying,
title = {{Certifying Hidden Dissipation from Observed Current Fluctuations}},
author = {Ahmed Roman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12598},
eprint = {2609.12598},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12598},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Certifying Hidden Dissipation from Observed Current Fluctuations
AU - Ahmed Roman
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12598
UR - https://arxiv.org/abs/2609.12598
AB - A single-molecule experiment on a driven enzyme or motor resolves only a few of the transitions the machine makes, yet one would like to know how much free energy it dissipates in total, including on the steps that stay hidden. The mean and the fluctuations of the currents on the watched transitions are shown to certify this hidden dissipation, with no knowledge of the transition rates and no access to the hidden transitions: when the watched transitions span the cycles of the network, the observed-current covariance recovers the full density-contracted quadratic current geometry, including the contribution of transitions that are never seen. The mechanism is that fluctuations are set by the dynamical activity, or traffic, the symmetric partner of the current. Contracting the large-deviation cost of empirical currents over density fluctuations identifies the observed-current covariance with a traffic-weighted metric, and turns partial observation into a minimum-energy completion problem over the unseen cycles, whose solution is the certified hidden cost. Existing current-fluctuation uncertainty relations bound dissipation from chosen currents but do not say when partial observation fixes the hidden contribution; the cycle-observability condition derived here does. The statements concern long-time means and fluctuations; finite-time estimates require separate error control.
ER -