Thermodynamic Uncertainty Relation For a Multi-Phase Alternating Renewal Random Walk
Abstract
Thermodynamic Uncertainty Relations (TURs) impose universal bounds linking current precision to entropy production in nonequilibrium systems. While general bounds like the Proesmans--Van den Broeck (PV) relation provide a broad framework, they often remain loose for processes characterized by renewal events. In this work, we derive a generalized entropic bound for current fluctuations in renewal-reward processes. By utilizing a rigorous variance decomposition within the framework of renewal-reward theory, we obtain a model-independent bound that is not only rigorous but tighter than the standard PV relation. Notably, in the linear-response regime, our bound correctly scales with the renewal rate and identifies a precision penalty arising from cycle-length fluctuations. These results provide a physically informative constraint on the precision of run-and-tumble-type dynamics and highlight the universal limits of transport in complex stochastic walkers.
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BibTeX
@misc{karimi2026thermodynamic,
title = {{Thermodynamic Uncertainty Relation For a Multi-Phase Alternating Renewal Random Walk}},
author = {Fatemeh Karimi and Farhad H. Jafarpour},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.16339},
eprint = {2606.16339},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.16339},
}
RIS
TY - UNPB
TI - Thermodynamic Uncertainty Relation For a Multi-Phase Alternating Renewal Random Walk
AU - Fatemeh Karimi
AU - Farhad H. Jafarpour
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2606.16339
UR - https://arxiv.org/abs/2606.16339
AB - Thermodynamic Uncertainty Relations (TURs) impose universal bounds linking current precision to entropy production in nonequilibrium systems. While general bounds like the Proesmans--Van den Broeck (PV) relation provide a broad framework, they often remain loose for processes characterized by renewal events. In this work, we derive a generalized entropic bound for current fluctuations in renewal-reward processes. By utilizing a rigorous variance decomposition within the framework of renewal-reward theory, we obtain a model-independent bound that is not only rigorous but tighter than the standard PV relation. Notably, in the linear-response regime, our bound correctly scales with the renewal rate and identifies a precision penalty arising from cycle-length fluctuations. These results provide a physically informative constraint on the precision of run-and-tumble-type dynamics and highlight the universal limits of transport in complex stochastic walkers.
ER -