Irreversibility from Self-Reference: Gradient Flow and an H-Theorem for a Self-Referential Statistical Operator Framework (opens in new tab)

This paper is a direct companion to arXiv:2605.06705, where the self-referential operator Omega was introduced and the Tsallis index q = alpha + beta was derived as a fixed-point condition within the local kernel approximation (LKA). Here we address four aspects deferred from the previous work. First, we carry out the first-order perturbative expansion of Omega beyond the LKA and demonstrate structural stability of q = alpha + beta at leading or...