Emergent Spacetime and the Thermodynamic Origin of Time: An Extension of the Indivisible Stochastic Framework

We extend Barandes’ indivisible stochastic interpretation of quantum mechanics to address the emergence of classical spacetime and the arrow of time from collective quantum processes. While Barandes (2025) demonstrates that individual quantum sys- tems can be understood as indivisible stochastic processes, we show that when many such systems interact, their collective behavior generates emergent spatial structure through quantum correlations and emergent temporal divisibility through thermody- namic irreversibility. Specifically, we argue that: (1) spatial relations emerge from patterns of quantum entanglement and correlation among multiple actualizations; (2) thermodynamic entropy production in many-body systems creates an irreversible ar- row of time; (3) this irreversibility transforms the fundamentally indivisible quantum process into an apparently divisible classical process; and (4) the time parameter t itself emerges as a bookkeeping device for tracking these irreversible collective changes. This framework provides a unified account of the quantum-to-classical transition, connect- ing quantum foundations, statistical mechanics, and emergent spacetime in a coherent picture where both space and time arise from the collective dynamics of indivisible quantum actualizations.