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| Format: | Preprint |
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2025
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| Accès en ligne: | https://arxiv.org/abs/2511.04022 |
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| _version_ | 1866909909355855872 |
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| author | Bennett, Justin |
| author_facet | Bennett, Justin |
| contents | Transport networks must balance viscous pumping losses with the energetic cost of maintaining an operative architecture. This paper formulates that trade-off as an entropy-per-information-cost (EPIC) extremum that prices structural upkeep in calibrated units (joules per bit). An upkeep law r^m distinguishes volume-priced (m = 2) from surface-priced (m = 1) maintenance. In laminar Poiseuille flow, stationarity yields (i) a generalized Murray scaling Q proportional to r^alpha with alpha = (m + 4)/2; (ii) a tariff-weighted vector balance that fixes bifurcation geometry and predicts near-symmetric daughter openings of about 75 degrees for m = 2 and about 97 degrees for m = 1; and (iii) a universal partition of power between pumping and upkeep. Eliminating radii gives a strictly concave flux cost proportional to Q^gamma with gamma = 2m/(m + 4), favoring mergers and deep tree hierarchies, and defines a routing index that induces Snell-like refraction of optimal paths across spatial tariff contrasts. A preregistered, held-out test on retinal bifurcations from the High-Resolution Fundus dataset (N = 19,126) shows sharp vector closure: the median residual is R = 0.232 with a nonparametric 95 percent bootstrap interval [0.229, 0.236], 91 percent of junctions fall under the pre-specified strict threshold, and structure-preserving nulls shift decisively to larger residuals. These results render classical branching relations explicitly unit-bearing (J/bit) and provide falsifiable geometric targets and quantitative design rules for transport networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04022 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Murray's Law as an Entropy-per-Information-Cost Extremum Bennett, Justin Biological Physics Transport networks must balance viscous pumping losses with the energetic cost of maintaining an operative architecture. This paper formulates that trade-off as an entropy-per-information-cost (EPIC) extremum that prices structural upkeep in calibrated units (joules per bit). An upkeep law r^m distinguishes volume-priced (m = 2) from surface-priced (m = 1) maintenance. In laminar Poiseuille flow, stationarity yields (i) a generalized Murray scaling Q proportional to r^alpha with alpha = (m + 4)/2; (ii) a tariff-weighted vector balance that fixes bifurcation geometry and predicts near-symmetric daughter openings of about 75 degrees for m = 2 and about 97 degrees for m = 1; and (iii) a universal partition of power between pumping and upkeep. Eliminating radii gives a strictly concave flux cost proportional to Q^gamma with gamma = 2m/(m + 4), favoring mergers and deep tree hierarchies, and defines a routing index that induces Snell-like refraction of optimal paths across spatial tariff contrasts. A preregistered, held-out test on retinal bifurcations from the High-Resolution Fundus dataset (N = 19,126) shows sharp vector closure: the median residual is R = 0.232 with a nonparametric 95 percent bootstrap interval [0.229, 0.236], 91 percent of junctions fall under the pre-specified strict threshold, and structure-preserving nulls shift decisively to larger residuals. These results render classical branching relations explicitly unit-bearing (J/bit) and provide falsifiable geometric targets and quantitative design rules for transport networks. |
| title | Murray's Law as an Entropy-per-Information-Cost Extremum |
| topic | Biological Physics |
| url | https://arxiv.org/abs/2511.04022 |