Competing and complementary models of resting-state brain dynamics contribute to our phenomenological and mechanistic understanding of whole-brain coordination and communication, and provide potential evidence for differential brain functioning associated with normal and pathological behavior. These neuroscientific theories stem from the perspectives of physics, engineering, mathematics, and psychology and create a complicated landscape of domain-specific terminology and meaning, which, when used outside of that domain, may lead to incorrect assumptions and conclusions within the neuroscience community. Here we review and clarify the key concepts of Connectivity, Computation, Criticality, and Coherence — the 4C’s — and outline a potential role for metastability as a common denominator across these propositions. We analyze and synthesize whole-brain neuroimaging research, examined through functional magnetic imaging (fMRI), to demonstrate that complexity science offers a principled and integrated approach to describe, and potentially understand, macroscale spontaneous brain functioning.

Healthy brain functioning depends on balancing stable integration between brain areas for effective coordinated functioning, with bursts of desynchronisation to allow subsystems to reconfigure and express functional specialisation. Metastability, a concept originated in statistical physics and dynamical systems theory, has been proposed as a key signature that characterises this balance. Building on this principle, the neuroscience literature has employed markers of metastability to investigate various aspects of brain function including cognitive performance, healthy ageing, meditation, sleep, responses to pharmacological challenges, and to characterise psychiatric conditions or disorders of consciousness. However, this body of work often uses the notion of metastability heuristically, and sometimes inaccurately, making it hard for the uninitiated to navigate the vast literature, interpret findings, and foster further development of theoretical and experimental methodologies. In this paper we provide a comprehensive review of metastability and its applications in neuroscience, covering its scientific and historical foundations and the practical estimators used to estimate it in empirical data. We also provide a critical analysis of recent theoretical developments, clarifying common misconceptions and paving the road for future developments.

Five fundamental problems—neutrino mass, baryogenesis, dark matter, inflation, strong CP problem—are solved at one stroke in a model, dubbed as “SM-A-S-H” (Standard Model-Axion-Seesaw-Higgs portal inflation) by Andreas Ringwald et. al. The Standard Model (SM) particle content is extended by three right-handed SM-singlet neutrinos $N_i$, a vector-like color triplet quark $Q$, a complex SM-singlet scalar field $\sigma$ that stabilises the Higgs potential, all of them being charged under Peccei-Quinn (PQ) $U(1)$ symmetry, the vacuum expectation value $v_\sigma\sim10^{11}$ GeV breaks the lepton number and the Peccei-Quinn symmetry simultaneously. We found that numerically SMASH model not only solves five fundamental problems but also the sixth problem “Vacuum Metastability” through the extended scalar sector and can predict approximately correct atmospheric neutrino mass splitting around 0.05 eV and the solar neutrino mass splitting around 0.009 eV.