Cyclones and Starswirls: Two Scales of Prigogine Dissipative Structures Galactic Rotation Curves and Accelerated Cosmic Expansion in the GEE Framework

Abstract This paper proposes a phenomenological framework (GEE framework) based on gravitational dissipative structures and the holographic principle, interpreting the observational effects known in the standard cosmological model as "dark matter" and "dark energy" as effective projections of gravitational degrees of freedom during coarse-graining. The core physical picture of this paper is the isomorphic manifestation of Prigogine dissipative structures at two scales: at the thermodynamic scale, the most universal Prigogine dissipative structure is the cyclone; at the gravitational scale, the most universal manifestation is the starswirl isomorphic to the cyclone structure. Earth's typhoons, Jupiter's Great Red Spot, Mars' global dust storms, and Venus' polar vortices are all quasi-steady ordered structures formed by open systems relying on continuous energy flow, far from equilibrium, and self-organizing through nonlinear positive feedback. The Milky Way, galaxy clusters, and accretion disks are quasi-steady rotating structures formed by self-gravitating systems during virialization. Under the Prigogine framework, both share the same abstract structure: open system, far from equilibrium, nonlinear positive feedback, continuous entropy production, self-organized ordered structure. The physical identity of the GEE framework is precisely the Prigogine dissipative structure theory in long-range force systems. However, structural isomorphism does not equal physical equivalence. From cyclone to starswirl, there exist three hard breaks: first, opposite signs of heat capacity — the cyclone is a positive heat capacity system, the starswirl is a negative heat capacity system; second, different energy currencies — the cyclone corresponds to thermal energy of the canonical system, the starswirl corresponds to gravitational potential energy of the microcanonical system; third, a time scale difference of about 20 orders of magnitude — cyclone lifetimes are on the order of days to a century, starswirl lifetimes are on the order of hundreds of millions of years. Among the three breaks, only the second can be softened through temperature equivalence. This paper defines Here is the local gravitational temperature in the microcanonical ensemble sense, approximately equal to the microcanonical statistical temperature when the self-gravitating system reaches local thermal equilibrium; under the virial approximation, it is equivalent to the dynamical temperature is the ratio of the two temperature scales, used to compare the local gravitational potential depth with the thermal motion energy density; it does not represent a phase transition between two thermodynamic temperatures. has negative heat capacity and does not possess a stable thermodynamic limit of the canonical ensemble; is the canonical ensemble thermodynamic temperature. The first and third breaks remain hard breaks: negative heat capacity solves the mechanical stability problem of the starswirl, but does not solve the energy source problem; the starswirl still requires external energy flows , to maintain the far-from-equilibrium state, so that entropy production persists. The cyclone and starswirl are isomorphic in mathematical form, but have opposite signs of heat capacity: after the cyclone's energy flow is cut off, decreases causing to rise and the structure to collapse; after the starswirl's energy flow is cut off, rises causing to rise, but the structure is maintained due to negative heat capacity self-regulation. The two are two ends of the dissipative structure spectrum, not the same mechanism; this paper calls this "structural isomorphism, mechanism opposition." As a Prigogine dissipative structure, the starswirl likewise requires continuous external energy flow, and the input energy required to maintain the dissipative structure is at least several times the dissipation; the main energy supply in late times is cosmic expansion energy . Negative heat capacity only solves the mechanical stability problem of the starswirl, not the energy source problem.