Geometric Overflow: The Emergence of Irreversibility

Files https://doi.org/10.5281/zenodo.19010664

Authors/Creators

• SEERAVERSE Research Group¹
• Tajima, Seera¹

Description

In the preceding toy formulation of Selection Geometry, local reduced mixedness
was introduced as a first quantitative proxy for geometric overflow: the structural
excess that remains inaccessible under observer-dependent realization.

In this paper, we argue that such overflow provides a natural route to the emergence of irreversibility.

While the global state evolves unitarily and remains fully coherent,
the realized local sector is obtained only through observer-dependent reduction,
and this reduction is generically non-invertible.

As a consequence, realized evolution is not most naturally described by a reversible group structure, but by a
semigroup-like ordering of accessible states. We propose that this structural asymmetry
underlies the appearance of local mixedness, loss of reversibility, entropy-like
growth, and thermality-like behavior without requiring any fundamental breakdown
of global quantum evolution or the ad hoc introduction of stochastic collapse mechanisms.

On this view, irreversibility is neither imposed by external coarse-graining
nor merely an epistemic artifact of human ignorance, but emerges from geometric
overflow itself: what cannot be locally re-accessed reappears operationally as directional
temporal order.

Geometric overflow is thereby advanced as a structural
bridge between reversible quantum possibility and irreversible realized history.