Abstract
The boundaries between physics, chemistry, and biology have long been defined by apparent differences in organizational complexity and information processing capabilities. Here, we present a universal mathematical framework that dissolves these artificial distinctions by proving that three major theoretical approaches—Classical Thermodynamics, Friston's Free Energy Principle, and the Maximum Entropy Production Principle (MEPP)—are mathematically equivalent formulations of a single optimization principle through a universal variational principle δΦ[S,C]/δS = 0, where Φ represents entropy production efficiency under different constraint regimes. Physical systems universally maximize entropy production rates through optimization of Ω accessible (S, 𝒞 ,t)/K(S observed , 𝒞 ,t), where Ω accessible represents accessible configurations within a constituent framework 𝒞 (observer-constructed measurement groupings), and K represents the Kolmogorov complexity of observed trajectories.
Experimental validation using the Belousov-Zhabotinsky chemical oscillator demonstrates that organized states enhance entropy production by factors of (1.2 ± 0.3) × 10000 compared to random molecular motion. Multi-observer protocols confirm that the same physical system displays different apparent memory capabilities, with M(S,t|O) = α log(Ω accessible ) - β K(S observed ) + γ varying systematically with the observer's dimensional access ratio D obs /D total , where D obs represents dimensions accessible to the observer and D total represents the system's true dimensionality. These results validate both the objective optimization process and the observer-dependent emergence of cognitive phenomena, demonstrating that what we interpret as "memory," "learning," and "intelligence" are not intrinsic system properties but arise from dimensional limitations of observation.
Our analysis reveals that the current third law of thermodynamics provides only a passive description of zero-temperature limits. We demonstrate that this law emerges as a special case of a more fundamental active principle: systems evolve to maximize entropy production rate dS/dt through optimization of Ω accessible (S, 𝒞 ,t)/K(S observed , 𝒞 ,t) until available energy gradients are exhausted. This active principle explains why organization enhances rather than opposes entropy production, resolving the long- standing paradox of biological complexity within thermodynamic constraints.