by William Brookfield

Abstract—The ability of the Generalized Second Law to withstand singularity, suggests this putative super-law to be even more robust and fundamental than general relativity or quantum mechanics. Profound differences, however, in the derivations of the two components of the GSL (thermodynamics and black hole dynamics) suggest a need for a new unified conceptual framework. Since Ludwig Boltzman’s work in the late nineteen hundreds on statistical mechanics, there has existed the question of how the apparently time symmetric dynamic laws of Newton (and later Einstein) could coexist with the time asymmetric Second Law of thermodynamics (and later, black hole dynamics). Another unresolved problem is the question of how to apply Boltzman statistical thermodynamics to something as small as a single particle.

“Topological Devolution” is a non-statistical, space-time topology based, inverse formulation of the orthodox Second law. Along with making sense of the thermodynamic arrow at the particle level, the TD model automatically includes a space-time compressant “the devolutionary potential.” This energy potential looks and behaves suspiciously like the Ricci curvature tensor of General Relativity. Furthermore, as a byproduct of this fundamental potential, many other features of a relativistic universe seem to be appearing. This seems to be more than just coincidence. If true, the GSL is the most fundamental law and force in the physical cosmos.

The name “Devolution” like its antithesis “Evolution” refers to cumulative change (of order content) over time. The Devolutionary arrow, however, points in the opposite direction to that of “Evolution.” I have decided to use this particular name due to the immediate understanding of both the meaning and the implications of this new law and most fundamental cosmological force.

The paper is divided into three parts;
Part One -- “The Physical Incompleteness Theorem -- Verification of the Cosmic Arrow.” In Part One my argument is statistical in nature. I first determine the source of directional uncertainty and recurrences in finite, partially random systems and finite thermodynamic systems. I then proceed to an examination of the physical universe as a whole, seeking an equivalent source of directional uncertainty. Finding no source of uncertainty, I thus confirm, for the universe as a whole, the singular directionality of the Cosmological Second Law and “The Physical Incompleteness Theorem.”

Part Two -- In “A Murphylian Second Look at the Second Law” I provide an examination and analysis of the theoretical difficulties and challenges of the Second Law of Thermodynamics in finite systems. I take a perhaps unexpected, approach to the local Second “Law” employing “Murphy’s Law” as a temporarily alternative. Through the use of “Murphylian Analysis” I argue for the existence a more fundamental physical law behind the presently uncertain Second Law of Thermodynamics.

Part Three -- “The Devolving Gas, The Devolving Cosmos - An Introduction to Topological Devolution.” I propose a non-statistical topo-dynamic alternative the Second Law and show how this model automatically leads to a devolutionary, general relativistic, black hole dynamic universe.

The full paper is available below:
In Search of a Cosmic Super-Law: The Supreme “Second law” of Devolution