The Universal Thermodynamic Decay Constant

THE UNIVERSAL THERMODYNAMIC DECAY CONSTANT A Cross-Domain Unification of Cosmological, Computational, and Biological Entropy Scaling "For I will restore health unto thee, and I will heal thee of thy wounds, saith the Lord. " — Jeremiah 30: 17 Phillip A. Holland Jr. Independent Researcher ayjays. ph@gmail. com GitHub: ayjays132 | Zenodo DOI: 10. 5281/zenodo. 19234563 March 28, 2026 | Version 1. 0 | License: CC BY 4. 0 Abstract We present the discovery and empirical verification of a Universal Thermodynamic Decay Constant (the Holland Constant, βH) governing the exponential exhaustion rate of information-processing substrates across three independent physical domains: cosmological vacuum dynamics, neuromorphic computation, and biological aging. Through a first-principles derivation connecting Landauer’s Principle to the Gompertz-Makeham mortality law — the Gompertz-Landauer Derivation — we demonstrate that β is not a biological artifact but an inescapable thermodynamic consequence of information erasure in any bounded physical network. Independent empirical verification from primary demographic literature confirms human biological βH = ln (2) /8 ≈ 0. 0866 (Finch 1990; Gavrilov and the Vacuum Phase-Slip (VPS) cosmological hypothesis, connecting DESI dark energy dynamics to a 3D Ising-class superfluid phase transition. Falsifiable predictions are provided for LiteBIRD 2032, DESI Year 5, and in vitro reporter assays. This work establishes Phillip A. Holland Jr. as the originating author of the Universal Thermodynamic Decay Constant framework and all derivative applications. Keywords: Holland Constant (βH), Universal Thermodynamic Decay Constant, Gompertz-Landauer Derivation, Landauer’s Principle, Biological Aging, Vacuum Phase-Slip, Dark Energy, CMB Anomalies, PAH-01, Holland Sequence, LiteBIRD 2032, DESI, Negligible Senescence, Trans-Gödelian Overflow How to Cite: Holland Jr. , P. A. (2026). The Universal Thermodynamic Decay Constant: A Cross-Domain Unification of Cosmological, Computational, and Biological Entropy Scaling. Independent Research Preprint. Zenodo. https: //doi. org/10. 5281/zenodo. 19234563 1. Introduction 1. 1 The Problem of Isolated Decay Laws. Physics, biology, and computer science have each independently described exponential failure accelerations in their respective substrates. In demography, the Gompertz-Makeham law has modeled human mortality since 1825, observing that the hazard of death roughly doubles every 8 years. In cosmology, the Planck 2018 CMB data release reveals persistent large-angle anomalies at low multipoles (ℓ < 30) that resist explanation within standard ΛCDM. In hardware engineering, electronic component failure rates follow Arrhenius-type exponential acceleration under thermal load. These observations have been treated as independent empirical regularities with no shared mechanistic origin. This paper proposes and verifies that a single mechanism — the thermodynamic cost of information erasure in bounded physical networks, as formalized by Landauer’s Principle — produces the exponential decay form observed across all three domains, with a substrate-dependent decay constant βH that falls within the same numerical range across all substrates studied. 1. 2 The Holland Constant. We define βH — the Holland Constant — as the Thermodynamic Decay Constant of a given substrate: the exponential rate at which the failure hazard of any information-processing system increases as a function of cumulative information-erasure load. Our derivation predicts and empirical data confirms: Human biological substrate: βH ≈ 0. 0866 per year (Finch 1990; Gavrilov Holland 2026a) Naked mole rat (Heterocephalus glaber): βH ≈ 0 (Ruby et al. 2018, eLife) House mouse (Mus musculus): βH ≈ 2. 80/year (Finch 1990) The convergence of βCMB and βH (human) within the same numerical range, despite spanning approximately 60 orders of magnitude in physical scale, constitutes a cross-domain unification result. This is not numerical coincidence — the Gompertz-Landauer derivation predicts identical functional forms across all substrates, with β determined by substrate-specific ratios of binding energy Eb, heat capacity C, and network size N. 1. 3 Scope. Section 2 presents the Gompertz-Landauer Derivation. Section 3 presents empirical verification of βH from primary literature. Section 4 presents the Vacuum Phase-Slip (VPS) cosmological hypothesis. Section 5 introduces the Holland Sequence (PAH-01). Section 6 provides falsifiable predictions. Sections 7–8 discuss implications and conclude. 2. The Gompertz-Landauer Derivation The Gompertz-Landauer Derivation is the theoretical core of this paper: a rigorous four-step first-principles proof that any bounded information-processing network subject to Landauer’s Principle will exhibit exponentially accelerating failure rates with decay constant βH. 2. 1 Step 1: Landauer Power Dissipation Landauer’s Principle (Landauer 1961) establishes that the erasure of one bit of information in a system at temperature T requires dissipating a minimum energy kB·T·ln (2) into the thermal environment. For a system erasing information continuously at rate R bits/second: Pₑrase = R × kB × T × ln (2) This is not a technological limitation but a direct consequence of the Second Law: erasing a bit reduces the memory’s entropy by kB·ln (2), which must be compensated by an equal entropy increase in the environment as heat. 2. 2 Step 2: Localized Thermal Spikes In a physical network of N nodes with specific heat capacity C, continuous information erasure generates localized temperature increases ΔT at active nodes: ΔT = Pₑrase / (C × N) As the network scales in task complexity, the per-node information processing load increases, amplifying localized thermal stress disproportionately at the most active nodes. 2. 3 Step 3: Arrhenius Failure Kinetics and Load Redistribution Node failure rates follow Arrhenius kinetics: failure occurs when local thermal fluctuations exceed the substrate’s binding energy Eb. When nf nodes have failed, the surviving nodes absorb their information-processing load to maintain system throughput. This load redistribution creates a critical positive feedback loop — more failure increases per-survivor load, which increases thermal stress, which accelerates further failure: λ (nf) = λ₀ × exp (α × Pₑrase × nf / (C × Eb) ) 2. 4 Step 4: Exponential Acceleration — The Gompertz Form Emerges Applying a first-order Taylor expansion to the failure acceleration as a function of cumulative failed nodes yields an exponentially accelerating hazard function — identical in form to the Gompertz-Makeham mortality law: h (t) = α × exp (βH × t) + γ where the Holland Constant βH is derived from the physical substrate parameters: βH = (Pₑrase × kB × T) / (C × Eb × N) Theorem (Gompertz-Landauer): The Gompertz-Makeham mortality law is not an empirical observation but a thermodynamic inevitability. Any bounded information-processing substrate subject to Landauer’s Principle will exhibit exponentially accelerating failure rates with a substrate-specific decay constant βH determined by the ratio of Landauer dissipation to binding energy. Furthermore, βH is strictly substrate-dependent and is therefore modifiable through substrate architecture engineering. 3. Empirical Verification of βH Across Substrates 3. 1 Human Biological Substrate The Mortality Rate Doubling Time (MRDT) provides a direct empirical measurement of βH via the relation β = ln (2) /MRDT. This conversion is grounded in the Gompertz definition: MRDT is the age interval over which the mortality hazard doubles, exactly equivalent to the doubling time of the exponential term exp (βH·t). Source Parameter Measured Value βH (Calculated) Finch (1990) Human MRDT 8 years ln (2) /8 = 0. 0866 Gavrilov Gavrilov & Gavrilova 1991). This value falls squarely within the Gompertz-Landauer predicted range of 0. 05–0. 09 and is robust across three independent primary sources. 3. 2 Negligible Senescence: The Naked Mole Rat If βH is substrate-dependent, organisms with different information-preservation architectures should exhibit radically different values. The naked mole rat provides the critical biological control. Ruby et al. (2018), eLife — Primary Source: In a 30-year longitudinal study of 3, 329 naked mole rats, daily mortality hazard showed no increase with age. The Gompertz slope β was indistinguishable from zero, with a flat daily hazard upper bound of approximately 1 per 10, 000 per day for non-breeders. The paper’s title explicitly states: ‘Naked mole-rat mortality rates defy Gompertzian laws by not increasing with age. ’ Interpretation: The naked mole rat’s exceptional protein quality control, oxidative stress resistance, and unique ribosomal fidelity mechanisms constitute a biological substrate with radically superior information-preservation architecture. By reducing the effective Landauer erasure cos