Relational Probability Fields: Coherence, Collapse and Cross-Domain Patterns

We introduce the notion of relational probability fields: probability distributions over discrete sets of possibilities that are shaped by context-dependent relational potentials and resolved by collapse or flow mechanisms. We show that quantum measurements (via the Born rule), Boltzmann ensembles in statistical mechanics, next-token prediction in large language models, Bayesian updating and evolutionary game dynamics can all be written in this common language. In each case, a field of possibilities, a relational potential (Hamiltonian, logit, likelihood, fitness) and a selection rule jointly determine which configurations are realised, amplified or suppressed. On this structural basis, we formulate a speculative hypothesis: that the probabilities appearing in these formalisms can be interpreted as measures of relational coherence or fit between configurations and their context, and that collapse can be viewed as a form of coherence optimisation on such fields. In particular, we suggest that Born probabilities |⟨λᵢ|ψ⟩|² quantify how strongly the joint system–apparatus configuration projects onto each eigenstate in Hilbert space geometry, while Boltzmann weights and softmax scores play an analogous role in energy and representation spaces. We outline how this coherence-based reading of probabilities may offer a more unified perspective on probabilistic laws and may connect naturally to information-theoretic and variational approaches to gravity, in which spacetime dynamics is driven by extremal principles on relational structures. The paper is primarily conceptual. It does not propose a new microphysical theory, nor does it derive the Born rule or Einstein’s equations from a single principle. Rather, it makes explicit a recurring organisational pattern in existing theories and suggests that interpreting probabilities as relational coherence may provide a useful template for future work at the interface of quantum theory, statistical mechanics, machine learning and gravitational physics.