The recent experimental observation of thermal rectification in a graphite Tesla valve suggests a phonon hydrodynamic mechanism beyond linear regime whose physical origin remains yet elusive. Here we uncover the correlation between nonreciprocal heat transfer and nonlinear phonon hydrodynamics by directly solving the nonlinear phonon Boltzmann transport equation with first-principles input. Pronounced thermal rectification and an unexpected crossover are unveiled in a prototypical asymmetric graphite ribbon. We reveal two underlying nonlinear effects including large phonon drift velocity and temperature-dependent phonon scattering rates which are dominant in hydrodynamic and diffusive regimes, respectively. Furthermore, the crossover behavior in graphite is shown to be governed by the competition between collective phonon drift and phonon excitation. This work thus establishes a theoretical framework for nonreciprocal phonon heat transport in nonlinear hydrodynamic regime and offers guidance for future theoretical and experimental studies on thermal functional devices based on collective phonon flow.

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• Collective behavior
• Phonons
• Thermal transport
• Boltzmann theory