Proper analysis of electron collisions in two spatial dimensions leads to the conclusion that the odd harmonics of the electron distribution function decay much slower than the even ones. At the same time, the number of long-lived odd harmonics quickly shrinks with increasing temperature. Focusing on a channel geometry with boundary scattering, we show that such behavior of the odd decay rates leads to a characteristic behavior of the conductance that we dub anomalous Knudsen effect: It initially grows with temperature but then starts to decrease, forming a peak. Further increase of the temperature forces the conductance to grow again because of the Gurzhi effect, associated with the crossover from ballistic to hydrodynamic transport. The simultaneous observation of the Gurzhi dip preceded by the anomalous Knudsen peak constitutes a particular signature of the long-lived modes in 2D electron transport at low temperatures.

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• Ballistic transport
• Electrical conductivity
• Two-dimensional electron gas
• Boltzmann theory