Hypothesis on the Emerint of Irreversibility from Geometric Overflow
Japanese Commentary
We propose that even when the global state remains reversible, phenomena such as temporal order, mixedness, and entropy increase can emerge if the reduction to the local region accessible to an observer is irreversible. This work attempts to describe the loss of accessibility through selection as the source of irreversibility.
Research Context
This is not intended to prove or replace standard theories in thermodynamics or the quantum measurement problem, but rather serves as a structural proposal for advancing mathematical verification.
Original Title: Geometric Overflow: The Emergence of Irreversibility
English Original
Files https://doi.org/10.5281/zenodo.19010664
Authors/Creators
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.