Extension of classical dynamics : emergence of irreversibility and stochasticity

Prigogine, Ilya, Elskens, Yves

M. Courbage

Reddy Govind

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.

Aritro Mukherjee

Abstract The deterministic and time-reversal symmetric dynamics of isolated quantum systems is at odds with irreversible equilibration observed in generic thermodynamic systems. Standard approaches at a reconciliation employ subjective restrictions on the space of observables or states and do not explain how a single macroscopic quantum system achieves equilibrium dynamically. We instead argue that quantum theory is an effective theory and requires corrections to accurately describe systems approaching the thermodynamic limit. We construct a stochastic extension of quantum theory which is practically identical to quantum mechanics for microscopic systems, yet allows individual macroscopic and isolated systems to objectively thermalize, generically. A fluctuation–dissipation relation guarantees physical consistency including norm preservation, energy conservation, no superluminal signalling and the emergence of microcanonical equilibrium. We further discuss the inclusion of objective collapse, thereby realizing a falsifiable theory of spontaneous universal irreversibility which describes the quantum-to-classical crossover dynamics of macroscopic quantum systems. The dynamics of the model describe spontaneous symmetry breaking, quantum state reduction and objective quantum thermalization for individual systems, while realizing emergent hybrid statistics for ensembles that integrate Born’s rule and microcanonical equilibrium.

E. B. Davies

Kevin ELLIS ANDERSON

This paper presents a regime-based account of discrete event formation within a variational dissipative–conservative framework in which irreversibility and constraint are primary. Discrete interaction events are shown to arise when multiple jointly persistent oscillatory continuations become dynamically incompatible under accumulating irreversible constraint. Event formation is not treated as a stochastic collapse mechanism, observer-dependent process, or additional postulate, but as the deterministic failure of coexistence once compatibility thresholds are exceeded. The work does not modify quantum mechanics, introduce hidden variables, or propose new dynamical laws. Its contribution is explanatory and foundational, providing the structural link between entanglement, decoherence, and the emergence of classical behaviour.