Thermodynamic response to evolution of erratic processes

Derive the full relations between changes in the parameters governing evolving erratic functions and the resulting changes in thermodynamic quantities such as entropy, internal energy, and temperature.

Background

The paper treats extrema statistics as snapshots of erratic processes and notes that the underlying process can evolve when parameters such as string-state partitioning or pinball-scattering asymmetries are varied.

Although the paper introduces effective thermodynamic quantities for the associated PDFs, it does not establish how parameter-driven evolution of the erratic function systematically maps to changes in entropy, energy, or temperature.

References

It seems plausible that such changes should be related to changes of the thermodynamical quantities like entropy, internal energy and temperature. The full relations between these two types of changes deserve a further research.

— Statistical Characterization of Erratic and Chaotic Processes through Their Extrema I. Thermodynamics  (2610.21620 - Sonnenschein, 15 Oct 2026) in Section Summary and future direction, final open-questions list