A non-equilibrium thermodynamics formulation of shear set-points in adaptively remodeling vascular networks
Abstract
Blood vessels remodel in response to wall shear stress while the network operates under a metabolic maintenance budget. For a power-law maintenance cost, minimizing dissipation at fixed budget yields a local shear set-point, and a purely local adaptation rule drives the network towards this optimum. Here we give this result a non-equilibrium thermodynamic formulation. Blood flow is an exactly linear Onsager system, and the slow remodeling of vessel radii is a gradient flow generated by a Rayleigh dissipation functional. This identifies the structural mobility, which scales inversely with the maintenance cost of each vessel and can be measured from radius fluctuations. Enforcing the budget exactly requires a time-dependent metabolic multiplier, which we obtain in closed form; with a fixed multiplier the budget is violated by up to one third during transients. The fluid displaced by remodeling vessels couples flow and structure through a symmetric, non-diagonal mobility, so that Onsager reciprocity becomes a testable statement: neighbouring vessels should show anticorrelated radius fluctuations. With noise, the structural sector obeys a second law and an integral fluctuation theorem. Non-reciprocal signaling between vessels, such as upstream conducted responses, then breaks the time-reversal symmetry of radius fluctuations and produces housekeeping entropy, detectable from time series of realistic length. Finally, we construct a partition function over network topologies with the number of loops as order parameter. Numerical tests show that loop counts do not collapse onto a single curve against an effective temperature, and that they depend strongly on the detection threshold.
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BibTeX
@misc{hernandezlemus2026nonequilibrium,
title = {{A non-equilibrium thermodynamics formulation of shear set-points in adaptively remodeling vascular networks}},
author = {Enrique Hernández-Lemus and Daniel Pérez-Calixto},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33250},
eprint = {2610.33250},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33250},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - A non-equilibrium thermodynamics formulation of shear set-points in adaptively remodeling vascular networks
AU - Enrique Hernández-Lemus
AU - Daniel Pérez-Calixto
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.33250
UR - https://arxiv.org/abs/2610.33250
AB - Blood vessels remodel in response to wall shear stress while the network operates under a metabolic maintenance budget. For a power-law maintenance cost, minimizing dissipation at fixed budget yields a local shear set-point, and a purely local adaptation rule drives the network towards this optimum. Here we give this result a non-equilibrium thermodynamic formulation. Blood flow is an exactly linear Onsager system, and the slow remodeling of vessel radii is a gradient flow generated by a Rayleigh dissipation functional. This identifies the structural mobility, which scales inversely with the maintenance cost of each vessel and can be measured from radius fluctuations. Enforcing the budget exactly requires a time-dependent metabolic multiplier, which we obtain in closed form; with a fixed multiplier the budget is violated by up to one third during transients. The fluid displaced by remodeling vessels couples flow and structure through a symmetric, non-diagonal mobility, so that Onsager reciprocity becomes a testable statement: neighbouring vessels should show anticorrelated radius fluctuations. With noise, the structural sector obeys a second law and an integral fluctuation theorem. Non-reciprocal signaling between vessels, such as upstream conducted responses, then breaks the time-reversal symmetry of radius fluctuations and produces housekeeping entropy, detectable from time series of realistic length. Finally, we construct a partition function over network topologies with the number of loops as order parameter. Numerical tests show that loop counts do not collapse onto a single curve against an effective temperature, and that they depend strongly on the detection threshold.
ER -