On the Irreversible Geometry of Order Parameter Space — The Principle of Minimum Irreversible Cost and Its Physical Consequences

This paper proposes a new theoretical framework for physical interactions, based on three core postulates. Postulate 1 (Principle of Minimum Irreversible Cost) states that the evolution path of an order parameter is determined by a joint variational principle involving the geometric kinetic energy and the Rayleigh dissipation function. Postulate 2 (Information Bottleneck Principle) provides a precise criterion for the quantum-classical boundary. Postulate 3 (Spacetime Emergence Hypothesis) uniquely determines a mapping from order parameter space to spacetime geometry. Core results include: a unified irreversible equation of motion that describes force, geometry, and entanglement in a single form; the metric gradient force, an exclusive new physical effect whose acceleration direction is independent of velocity sign; the information bottleneck theorem proving that irreversible classicality emerges when and only when dissipative channels open; five exhaustive projection types of physical effects; and the derivation of Einstein's field equations as an emergent consequence of order parameter dynamics at type-B penetrable singularities. Four exclusive quantitative predictions testable on current experimental platforms are provided. This principle does not replace Newtonian mechanics or general relativity, but delimits their domains of applicability and explains their origins. Quantum entanglement stability is guaranteed by the information bottleneck theorem.