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ABSTRACT: This paper presents a discrete spacetime model that establishes computable entropy coordinates to guide automaton evolution in alignment with thermodynamic causality. By defining entropy through multiplicative accumulation, the model ensures irreversible entropy increase while remaining consistent with conventional logarithmic entropy formulations. It further incorporates path selection rules derived from the least-action principle, enabling physically realistic evolution in discrete systems. The framework demonstrates broad consistency with observed phenomena, from quantum processes to relativistic effects, offering a new computational foundation for physics-based automata. Benchmark tests reveal significantly improved thermodynamic compliance compared to traditional simulation approaches.

Key words: multiplicative entropy; space-time-entropy mapping; thermodynamic time arrow; entropy coordinate;