Multiplicative Entropy | Analytic Quantum Thermodynamics
At the Planck scale , time has minimal intervals, making space transformations discrete. Thermodynamic transformations consequently become discrete as well, allowing analytical approaches to study thermodynamics at this fundamental level. The second law of thermodynamics describes energy homogenization as an entropy-increasing process. In a discrete quantum network model where each quantum carries energy while conserving total energy, the second law dictates energy transfer exclusively from higher-energy quanta to adjacent lower-energy ones. This process causes the product of energies (S = ∏ᵢ εᵢ) to increase monotonically, reaching its theoretical maximum when all quanta possess equal energy. Thus, using energy product as entropy measure perfectly aligns with the second law's quantum manifestation
The multiplicative entropy definition emerges naturally when mapping space transformations to the cumulative product of elementary quantum energies (εᵢ). By correlating these transformations with discrete time increments, both entropy and time acquire precise definitions. Each irreversible state transition of Space Elementary Quanta (SEQs) corresponds to entropy change, intrinsically linking temporal progression to entropy evolution. The logarithmic transformation lnS connects this formulation to conventional Boltzmann entropy while preserving its geometric interpretation for discrete systems.
This framework demonstrates how Planck-scale discreteness governs thermodynamic irreversibility through quantized energy redistribution, where minimal energy transfers (quantized in ±h units) drive the system toward maximum entropy configurations
