A Lennard-Jones gas confined by two parallel solid walls was studied using non-equilibrium Molecular Dynamics, where one-dimensional, steady heat flow was introduced through the gas. Under this condition, the velocity distribution in the direction of heat flow was found to develop skewness and the kurtosis was shown to increase with increasing gas density. In contrast, orthogonal velocity distributions presented no skewness but kurtosis was also found to deviate from equilibrium values. Analysis of statistics conditioned by the sign of molecular velocity showed that the difference in kinetic energy resulted in heat transfer. A proposed adiabatic feedback kurtosis controller, referred to as a kurtostat, manipulates velocity using a differential velocity scaling technique. This controller was used in a test setup to push the gas out of equilibrium without introducing heat flow, and it was found that velocity kurtoses were not independent but weakly coupled with a steady-state gain of approximately 0:16.
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