[Paper Review] Emergent deterministic systems

Ian T. Durham|arXiv (Cornell University)|Mar 4, 2017

Free Will and Agency3 citations

TL;DR

This paper demonstrates that deterministic macroscopic behavior can emerge from purely random microprocesses through combinatorial statistics, showing that even in fundamentally random systems, long-term aggregate behavior becomes predictable and stable. The key contribution is a mathematical framework illustrating how intentionality and free will-like behavior may arise naturally from randomness via statistical mechanics, without external forces or hidden determinism.

ABSTRACT

According to quantum theory, randomness is a fundamental property of the universe yet classical physics is mostly deterministic. In this article I show that it is possible for deterministic systems to arise from random ones and discuss the implications of this for the concept of free will.

Motivation & Objective

• To investigate whether deterministic behavior can emerge from fundamentally random processes without external forcing.
• To clarify the distinction between determinism, randomness, and causality in physical processes.
• To explore how free will might arise from randomness through combinatorial constraints on macroscopic outcomes.
• To examine whether internal system dynamics—specifically combinatorics—can impose boundary conditions that stabilize macroscopic behavior.
• To challenge the assumption that determinism is required for intentionality, proposing instead that partial determinism via statistics suffices.

Proposed method

• Models macroscopic behavior as the aggregate outcome of many random microprocesses, such as energy transfers in Einstein solids.
• Applies combinatorial statistics to calculate the relative probabilities of macrostates, showing that equilibrium states dominate due to high degeneracy.
• Defines 'partially deterministic' processes as those predictable in aggregate but not in individual instances, contrasting them with purely random or deterministic processes.
• Uses the example of a biased coin game (50.5% vs. 49.5%) to show that even small statistical advantages allow long-term predictability and profit, illustrating partial determinism.
• Analyzes thermal contact between two Einstein solids to show that random microprocesses lead to a stable, highly probable equilibrium macrostate through sheer combinatorial weight.
• Argues that combinatorics alone can act as a boundary condition, suppressing fluctuations and stabilizing macroscopic behavior without altering underlying microprocesses.

Experimental results

Research questions

• RQ1 Can deterministic behavior emerge from fundamentally random microprocesses through statistical aggregation?
• RQ2 What distinguishes partially deterministic processes from purely random or fully deterministic ones in physical systems?
• RQ3 Can free will emerge from randomness if macroscopic behavior is predictably stable due to combinatorics?
• RQ4 To what extent can internal system combinatorics impose boundary conditions on future macroscopic evolution?
• RQ5 Is the emergence of order and intentionality in the universe compatible with fundamental quantum randomness?

Key findings

• Even processes with only a 50.5% vs. 49.5% probability imbalance can yield predictable long-term outcomes, demonstrating that partial determinism is viable.
• The equilibrium state of two Einstein solids in thermal contact is overwhelmingly probable due to its high degeneracy, making fluctuations away from equilibrium unmeasurable.
• Combinatorics alone can stabilize macroscopic behavior by making certain macrostates vastly more likely, effectively imposing a boundary condition on future evolution.
• Random microprocesses (e.g., energy transfer between oscillators) continue indefinitely at equilibrium, yet the system remains macroscopically stable due to statistical dominance of the equilibrium state.
• The model shows that deterministic-like behavior—such as reliable profit in a biased game—can emerge from randomness without external control or hidden laws.
• The paper concludes that free will may not require determinism or randomness per se, but rather the capacity for partially deterministic, combinatorially constrained macroprocesses.