We bring together three key amplification mechanisms in linear dynamical systems: spectral criticality, resonance, and nonnormality. We present a unified linear framework that both distinguishes and quantitatively links these effects through two fundamental parameters: (1) the spectral distance to a conventional bifurcation or to a resonance and (2) a nonnormal index $K$ (or condition number $\kappa$) that measures the obliqueness of the eigenvectors. Closed-form expressions for the system's response in the form of the variance $v_{\infty }$ of the observable responding to both Gaussian noise and periodic forcing reveal a general amplification law $v_{\infty }=v_0(1+\mathcal{G}\left(K\right))$ with nonnormal gain $\mathcal{G}\left(K\right)\propto K^2$ represented in universal phase diagrams. By reanalyzing a model of remote earthquake triggering based on breaking of Hamiltonian symmetry, we illustrate how our two-parameter framework significantly expands both the range of conditions under which amplification can occur and the magnitude of the resulting response, revealing a broad pseudocritical regime associated with large $\kappa$ that previous single-parameter approaches overlooked. Similarly, in the non-Hermitian extensions of quantum optics provided by forward four-wave mixing experiments, we show the presence of a counterintuitive gain-from-loss effect that directly manifests nonnormal amplification in a propagating-wave setting. This predicts the possibility to engineer transient optical energy amplification without the need for true lasing or exact $\mathcal{PT}$-symmetry breaking. Our framework applies to many other physical, natural, and social systems and offers diagnostic tools to distinguish true critical behavior from transient amplification driven by nonnormality.

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• Brownian motion
• Classical statistical mechanics
• Critical phenomena
• Earthquakes
• Mathematical physics
• Nonequilibrium statistical mechanics
• Phase diagrams