Thermodynamic Analysis and Information-Theoretic Structure of the Nonhomogeneous 1D q -State Akin–Potts Model

This study investigates the thermodynamic and information-theoretic properties of a nonhomogeneous [Formula: see text]-state Akın–Potts hybrid model on an [Formula: see text]-lattice. We primarily utilize the transfer matrix formalism to construct the partition function for the one-dimensional lattice model. By decomposing the global transfer matrix into a product of submatrices that represent distinct interaction types, we analyze the equilibrium states of the system within a two-step transition framework and using the Kolmogorov–Chapman relation. Furthermore, we employ a gauge transformation that maps the physical transfer matrix onto a row-stochastic transition matrix, which enables the calculation of the entropy rate [Formula: see text] as a measure of the information production in the system. Unlike traditional homogeneous frameworks that rely on a single competing interaction, our model incorporates successively distinct coupling constants to better mimic the structural heterogeneities in real-world materials. We examine the interplay between these multi-coupling parameters and an external magnetic field, demonstrating how they govern the crossover from deterministic ordering at low temperatures to maximal stochasticity [Formula: see text] in the high-temperature limit. Notably, our findings reveal that this sequential interaction framework provides a highly tunable environment for modulating complex thermodynamic anomalies and pseudo-transitions, thereby offering a new source of inspiration for decoding non-homogeneous physical systems in modern condensed matter physics.