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We show that a hot rotating fluid of relativistic chiral fermions possesses anew gapless collective mode associated with coherent propagation of energydensity and chiral density waves along the axis of rotation. This mode, whichwe call the Chiral Heat Wave, emerges due to a mixed gauge-gravitationalanomaly. At finite density the Chiral Heat Wave couples to the Chiral VorticalWave while in the presence of an external magnetic field it mixes with theChiral Magnetic Wave. The coupling of the Chiral Magnetic and Chiral VorticalWaves is also demonstrated. We find that the coupled waves - which are coherentfluctuations of the vector, axial and energy currents - have generallydifferent velocities compared to the velocities of the individual waves.

Chiral Heat Wave and mixing of Magnetic, Vortical and Heat waves in chiral media