Nonlocal thermal noise in electrically coupled conductors: A microscopic two-dimensional study

What the math gives to ML

The paper identifies a concrete failure of the independent-local-noise approximation: capacitively coupled conductors held at different temperatures develop finite correlations between noise generated in distant segments, despite short-ranged microscopic interactions. Its transferable asset is a nonequilibrium fluctuation mechanism in which coupling creates off-diagonal noise covariance, while equilibrium or detached subsystems recover approximately independent Johnson noise. A neural-network analogue is to inject structured, block-correlated stochastic updates into coupled layers, parameter groups, or diffusion variables instead of assuming independent isotropic noise. The key experiment should test the predicted covariance transition under equal versus unequal effective temperatures and zero versus nonzero coupling.