Mathematical model of entropy S_Θ in the Acta Universi hypothesis

The Acta Universi (AU) hypothesis, proposed in 2025, models the S_Θ entropy as a key parameter integrating dark energy information density, collective consciousness, and entropic fluctuations. s_Θ is not a classical thermodynamic entropy (S = k ln W, where k is the Boltzmann constant, W is the number of microstates), but a generalized information entropy, where each bit of information is equivalent to energy according to the Landauer principle (E_bit = kT ln 2, with T being the temperature). In AU, s_Θ stimulates the expansion of the universe by resolvingthe Hubble tensionthrough positive curvature and the evolution of the dark energy equation of state w(a) = w_0 + w_a (1 - a), where a is the scale factor. The S_Θ model is hierarchical and evolves over time, reflecting the emergent structure of reality. Below I structure the model: definition, components, evolution equations, and derivation (as arriving at the solution). This is speculative, but it is based on the integration of the holographic principle (entropy is proportional to the area of the event horizon), entropic gravity (gravity as the entropy gradient), andthought forms ( formsnon-local operators).