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Galaxies obey a number of empirical correlations between their radio,{\gamma}-ray, and infrared emission, but the physical origins of thesecorrelations remain uncertain. Here we use the CONGRuENTS model for broadbandnon-thermal emission from star-forming galaxies, which self-consistentlycalculates energy-dependent transport and non-thermal emission from cosmic rayhadrons and leptons, to predict radio and {\gamma}-ray emission for a syntheticgalaxy population with properties drawn from a large deep-field survey. We showthat our synthetic galaxies reproduce observed relations such as the FIR-radiocorrelation, the FIR-{\gamma} correlation, and the distribution of radiospectral indices, and we use the model to explain the physical origins of theserelations. Our results show that the FIR-radio correlation arises because theamount of cosmic ray electron power ultimately radiated as synchrotron emissionvaries only weakly with galaxy star formation rate as a result of theconstraints imposed on gas properties by hydrostatic balance and turbulentdynamo action; the same physics dictates the extent of proton calorimetry indifferent galaxies, and thus sets the FIR-{\gamma}-ray correlation. We furthershow that galactic radio spectral indices result primarily from competitionbetween thermal free-free emission and energy-dependent loss of cosmic rayelectrons to bremsstrahlung and escape into galactic halos, with shaping of thespectrum by inverse Compton, synchrotron, and ionisation processes typicallyplaying a sub-dominant role. In addition to explaining existing observations,we use our analysis to predict a heretofore unseen correlation between thecurvature of galaxies' radio spectra and their pion-driven {\gamma}-rayemission, a prediction that will be testable with upcoming facilities.

CONGRuENTS (COsmic-ray, Neutrino, Gamma-ray and Radio Non-Thermal  Spectra). II. Population-level correlations between galactic infrared, radio,  and {\gamma}-ray emission