PreprintCC BY 4.0arXiv
A McLennan formula for equiaccessible steady states
Abstract
Near equilibrium, the Boltzmann distribution is corrected by the transient irreversible entropy flux, a result known as the McLennan formula. By expanding around equiaccessible steady states instead, we derive an analogue that can hold arbitrarily far from equilibrium. At zeroth order, steady-state occupation is determined solely by local escape rates, yielding a strong form of the active-matter principle of "low rattling." The first-order correction measures the impact of traffic imbalances on the accessibility of each state, marking the onset of nonlocal determinants of relative occupation.
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BibTeX
@misc{calvert2026mclennan,
title = {{A McLennan formula for equiaccessible steady states}},
author = {Jacob Calvert},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26755},
eprint = {2610.26755},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26755},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A McLennan formula for equiaccessible steady states
AU - Jacob Calvert
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.26755
UR - https://arxiv.org/abs/2610.26755
AB - Near equilibrium, the Boltzmann distribution is corrected by the transient irreversible entropy flux, a result known as the McLennan formula. By expanding around equiaccessible steady states instead, we derive an analogue that can hold arbitrarily far from equilibrium. At zeroth order, steady-state occupation is determined solely by local escape rates, yielding a strong form of the active-matter principle of "low rattling." The first-order correction measures the impact of traffic imbalances on the accessibility of each state, marking the onset of nonlocal determinants of relative occupation.
ER -