Quantum Entropic Relationalism (QER): Contemporary Debates and Theoretical Frontiers

Entropy has evolved from a secondary thermodynamic property (Clausius, 1865) to a potentially fundamental organizing structure of physical reality, particularly through its gravitational manifestation in the Bekenstein–Hawking formula. This article systematically reviews four theoretical developments (2015–2024) that test this hypothesis using analytical methods from quantum information theory, holographic duality, and quantum gravity. First, we examine how the quantum island formula (Equation (1)) resolves the black hole information paradox by demonstrating that fine-grained entropy depends on global causal structure rather than local degrees of freedom. Second, we analyze the Complexity = Volume and Complexity = Action conjectures, showing that computational complexity encodes post-thermalization dynamics on exponentially long timescales, with predicted maximum complexity Cmax∼eSBH testable in SYK simulations. Third, we examine the scope and limitations of three gravity frameworks (AdS/CFT holography, emergent gravity, loop quantum gravity) in addressing entropy’s role in initial conditions and extract their distinct observational signatures for 2025–2035 experiments. Fourth, we explore entropy–motion duality through mixed metric signatures; while the correspondence β↔it is suggestive, its full physical interpretation remains conjectural outside semiclassical and toy-model contexts. We articulate quantum entropic relationalism as an epistemological framework wherein entropy constitutes an objective relational structural property encoding physical relations without substantial reducibility. This synthesis suggests spacetime emerges from quantum entanglement substrates, with testability prospects via gravitational interferometry (LISA, Einstein Telescope), quantum simulators, and cosmological observations (Cosmic Microwave Background (CMB)-S4, LiteBIRD) anticipated by 2035.