The often overlooked role of sound in liquid thermal transport

Formulated a hundred years ago, the Bridgman formula for thermal conductivity of liquids postulates a proportionality between sound velocity and thermal conductivity and therefore appoints phonons as the main carriers of heat in a liquid. Its empirical success has been under-appreciated and its conceptual implications beyond the case of classical liquids has been overlooked. We review its origin, its links to hydrodynamic Euler equations and the fundamental paradox surrounding the parabolic heat equation and its fate across the quantum-classical crossover.