Structural Limitations of Classical Thermodynamics and the Introduction of a Complex Entropy General Equation

Classical thermodynamics provides a powerful framework for describing the relationship between energy and entropy, yet its applicability is structurally limited to diffusion-dominated phenomena near equilibrium. This paper clarifies the inherent limitations of classical thermodynamics in addressing real-world flow phenomena characterized by vortices, waves, boundaries, velocity differences, and nonequilibrium dynamics. To overcome these limitations, a ``complex entropy general equation'' is introduced by extending entropy into the complex domain. The real part represents diffusive behavior consistent with classical thermodynamics, while the imaginary part captures vortical, phase, restoring, and boundary-reflection structures. Using fire whirls as an illustrative example, the paper demonstrates how the interplay between local entropy decrease and global entropy increase generates velocity differences that give rise to rotational structures. Classical thermodynamics emerges as a special case corresponding to the real part of the general equation. The complex entropy general equation thus functions as a unified model for low-speed field phenomena beyond the reach of classical theory.