The Entropy Production of Galaxies

Abstract

Double-spiral galaxies are common in the Universe. It is known that the logarithmic double spiral is a Maximum Entropy geometry and represents spiral galaxies well. It is also known that the virial mass of such a galaxy can be approximately determined from the entropy of its central supermassive black hole. But over time the black hole must accrete mass, and therefore the overall galactic entropy must increase. From the associated entropic Euler-Lagrange equation (forming the basis of the Principle of Least Exertion, and also enabling the application of Nöther’s theorem) we show that the galactic entropy production is a conserved quantity, and we derive an appropriate expression for the relativistic entropic Hamiltonian of an idealised spiral galaxy. We generalise Onsager’s celebrated expression for entropy production and demonstrate that galactic entropy production has two parts, one many orders of magnitude larger than the other, and where the smaller is comparable to the Hawking radiation of the central supermassive black hole. We conclude that galaxies cannot be isolated, since even idealised spiral galaxies have non-zero entropy production.

The Poetics of Physics

“…Note that this is a simplified ("zeroth order") analytical approximation to reality: … the dynamics driving the galactic evolution [are neglected … but] this treatment gives the proper weight to the effect of the [central supermassive] black hole entropy Parker & Jeynes, 2019 Thus, the galactic shape is a primary geometric property, even if it can also be shown in standard treatments to emerge from the kinematics. Parker & Jeynes (2020) also prove that the stability of Buckminsterfullerene (C60) is a geometrical entropy property fundamentally related to its representation as a holomorphic object. They say that the stability of C60 is:…”

“…that information and entropy should be considered (contra Brillouin) not as opposites, but as complementary (that is, orthogonal in complex Minkowski 4-space). And indeed, they use the Shannon information entropy explicitly to discuss the stability of fullerenes: "So for example, for C60 … we can calculate an entropy … using the Shannon fragmentation metric" (Parker & Jeynes, 2020).…”

“…It turns out that there is an entropic counterpart to the Principle of Least Action: the Principle of Least Exertion. Parker & Jeynes (2020) explain: [Parker & Jeynes, 2019] have shown that the principle of least action has the entropic analogue of a principle of least exertion: where "action" is the path integral of the kinematic Lagrangian, "exertion" is the path integral of the entropic Lagrangian -which still satisfies the various canonical conjugate-pairing relationships. Roughly speaking, in the energy domain where the Hamiltonian represents the total energy of a system (that is, the sum of potential and kinetic terms), the Lagrangian represents an energy balance (the difference of potential and kinetic terms).…”

“…The "reflection" operation that yields the poem of Table 1 has a general importance. We have seen how Buckminsterfullerene (Parker & Jeynes 2020), and DNA and the Milky Way (Parker & Jeynes 2019) all have Maximum Entropy geometries precisely because these all involve holomorphic pairs: the logarithmic double spiral for the spiral galaxy, the double helix for DNA, a spherical double spiral for C60, and also, presumably, a pair of holomorphically bound "deuterons" for the alpha particle (Parker et al 2022). "Holomorphic" is used here in its full mathematical meaning but applied to real objects, which can therefore be realistically thought of as unitary objects.…”