Dissipative Gradient Dynamics: A Macroscopic Postulate and Its Mathematical Consequences

This study constructs a theoretical framework of dissipative gradient dynamics based on a single macroscopic empirical postulate: in an isolated system, differences among dissipative modes never grow and asymptotically tend to zero. By introducing the dissipative intensity field and the dissipative gradient field, and by defining the total irreversible difference functional, the corresponding coupled evolution equations are derived. A generalized H-theorem is proved: the total dissipative potential constitutes a strict Lyapunov functional of the system, guaranteeing that all inter-mode differences decay monotonically and approach the terminal anchor point. On the zero-sum subspace, global existence, uniqueness, and asymptotic convergence of weak solutions are established, and it is shown that physical extinction occurs within a finite time. Through a two-body decomposition of the many-body dynamics, the disturbance function that encodes many-body coupling is isolated. Its algebraic structure is shown to be universal across binary antisymmetric coupling systems, with testable predictions formulated in several physical domains. The equivalence among difference, force, and physical time is established as a rigorous consequence of the gradient-flow structure. Spectral analysis provides an operational definition of the characteristic length and proves the inevitable decay of high-pass difference energy. It is further found that many-body coupling can locally produce instantaneous reversal of the irreversible process, a phenomenon confirmed by direct numerical simulation. Formal extensions toward statistical field theory and quantization are briefly discussed.