Complexity Limits Resolve Singularities and Unify Gravity with Computation

Research establishes dynamical complexity as a fundamental postulate, yielding a smoothed entropy and resolving classical singularities. This framework unifies diverse phenomena, from critical points to black hole information, and predicts a relationship between universal complexity, holographic entropy, computation and gravity, linking action to circuit complexity and time to temperature.

The behaviour of systems undergoing phase transitions – from water boiling to materials becoming superconducting – has long presented theoretical challenges due to the emergence of singularities where conventional descriptions break down. Recent work proposes a resolution to these issues by incorporating the inherent limitations of information processing within thermodynamic systems. Researchers HongZheng Liu, YiNuo Tian, and Zhiyue Wu, all operating independently in China, detail this approach in their paper, “A Heuristic Study of Temperature: Quantum Circuitry in Thermal Systems”. Their analysis introduces ‘Complexity Windowed Thermodynamics’ (CWT). This framework posits a finite limit to the dynamical complexity required to define a system’s microstates, effectively smoothing out the singularities observed in classical thermodynamics and offering potential insights into areas ranging from critical phenomena to the information paradox surrounding black holes.

Complexity Limits Singularities, Unifying Thermodynamics, Gravity, and Computation

Classical physics predicts singularities – points where physical quantities become infinite – within black holes and at the universe’s beginning. These divergences typically arise from extrapolating current models to regimes demanding infinite computational resources for their complete description. We propose a framework where a finite ‘complexity budget’ fundamentally limits the accessible degrees of freedom within any system, thereby resolving these singularities and offering a unifying perspective on thermodynamics, gravity, and computation.

This complexity budget operates as a natural regulator. It posits that the universe, or any bounded system within it, possesses a finite capacity for storing and processing information. This limitation prevents the emergence of unphysical infinities and contributes to the overall stability of the universe. The budget isn’t a constraint on physics, but rather an inherent property of it.

Consider the black hole information paradox. Current theory suggests information falling into a black hole is lost, violating fundamental principles of quantum mechanics. Our framework suggests information isn’t destroyed, but rather encoded in subtle correlations within the outgoing Hawking radiation – the thermal radiation emitted by black holes. The complexity budget limits the information density within the black hole, forcing it to be distributed across the Hawking radiation, albeit in a highly scrambled form.

Furthermore, this approach suggests spacetime itself isn’t fundamental, but emergent. Spacetime arises from the underlying complexity of the universe, analogous to how temperature emerges from the collective behaviour of many particles. The more complex a system, the more intricate its emergent spacetime structure. This aligns with concepts explored in areas like loop quantum gravity and string theory, which also propose a discrete, rather than continuous, nature of spacetime at the Planck scale.

This framework extends beyond physics, offering insights into the emergence of time and consciousness. Time, we propose, isn’t a fundamental dimension, but an emergent property arising from the increasing complexity of the universe. Similarly, consciousness can be viewed as a particularly complex form of information processing, constrained by the brain’s complexity budget.

The complexity budget acts as a natural cutoff at high energies and densities, preventing the formation of naked singularities and ensuring the consistency of physical theories. This provides a novel approach to renormalisation – a technique used in quantum field theory to remove infinities arising from calculations.

Critically, they predict that the total complexity within a given volume of space is limited by the available computational resources within that volume. This implies the universe itself can be viewed as a vast computational system, processing information according to inherent constraints. This prediction offers a testable hypothesis. Future research could focus on quantifying the complexity of physical systems and searching for evidence of a finite complexity density in the universe. Measuring the complexity of quantum states, for example, could provide empirical support for this framework.