Thermodynamic Parametrisation of the Vertebrate Lifetime Cycle Invariant: Biological Proper Time, Allometric Mass-Cancellation, and Clade-Specific Predictions
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| Format: | Preprint |
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2026
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| author | Taye, Mesfin |
| author_facet | Taye, Mesfin |
| contents | Warm-blooded vertebrates accumulate approximately $\Nstar \approx 10^9$ cardiac cycles over a natural lifetime, a striking empirical regularity first quantified by Lindstedt and Calder yet lacking a physical interpretation. We propose that this invariance is consistent with a conserved thermodynamic budget, formulated here as the Principle of Biological Time Equivalence (PBTE). The framework rests on a constitutive closure $\dotΣ = σ_0 f$, which links the entropy production rate to the intrinsic physiological frequency; integration over the lifespan yields $Σ_{\mathrm{life}} = σ_0 \Nstar$, so that the observed constancy of $\Nstar$ corresponds to an approximately constant lifetime entropy budget. Algebraic exponent cancellation under Kleiber and Calder scaling laws, $\sigstar \propto M^{3/4+1/4-1}=M^0$, is consistent with mass-independence and reproduces the numerical value $N_0 \approx 1.52\times10^9$ without free parameters. The framework offers a thermodynamically consistent account of two outstanding problems: the origin of the numerical value of $\Nstar$ and the systematic deviations observed across clades. A multiplicative correction factor $Φ_C$, constructed from physiological determinants -- activity allocation, body temperature, mitochondrial efficiency, and extrinsic hazard -- predicts long-lived clades as regimes of reduced effective entropy production per cardiac cycle. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_24458 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Thermodynamic Parametrisation of the Vertebrate Lifetime Cycle Invariant: Biological Proper Time, Allometric Mass-Cancellation, and Clade-Specific Predictions Taye, Mesfin Statistical Mechanics Warm-blooded vertebrates accumulate approximately $\Nstar \approx 10^9$ cardiac cycles over a natural lifetime, a striking empirical regularity first quantified by Lindstedt and Calder yet lacking a physical interpretation. We propose that this invariance is consistent with a conserved thermodynamic budget, formulated here as the Principle of Biological Time Equivalence (PBTE). The framework rests on a constitutive closure $\dotΣ = σ_0 f$, which links the entropy production rate to the intrinsic physiological frequency; integration over the lifespan yields $Σ_{\mathrm{life}} = σ_0 \Nstar$, so that the observed constancy of $\Nstar$ corresponds to an approximately constant lifetime entropy budget. Algebraic exponent cancellation under Kleiber and Calder scaling laws, $\sigstar \propto M^{3/4+1/4-1}=M^0$, is consistent with mass-independence and reproduces the numerical value $N_0 \approx 1.52\times10^9$ without free parameters. The framework offers a thermodynamically consistent account of two outstanding problems: the origin of the numerical value of $\Nstar$ and the systematic deviations observed across clades. A multiplicative correction factor $Φ_C$, constructed from physiological determinants -- activity allocation, body temperature, mitochondrial efficiency, and extrinsic hazard -- predicts long-lived clades as regimes of reduced effective entropy production per cardiac cycle. |
| title | Thermodynamic Parametrisation of the Vertebrate Lifetime Cycle Invariant: Biological Proper Time, Allometric Mass-Cancellation, and Clade-Specific Predictions |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2604.24458 |