Life support with a mechanical ventilator is used to manage patients with a variety of lung diseases including acute respiratory distress syndrome (ARDS). Recently, management of ARDS has concentrated on ventilating at lower airway pressure using lower tidal volume. A large international study demonstrated a 22% reduction in mortality with the low tidal volume approach. The potential advantages of adding physiologic noise with fractal characteristics to the respiratory rate and tidal volume as delivered by a mechanical ventilator are discussed. A so-called biologically variable ventilator (BVV), incorporating such noise, has been developed. Here we show that the benefits of noisy ventilation - at lower tidal volumes - can be deduced from a simple probabilistic result known as Jensen’s Inequality. Using the local convexity of the pressure-volume relationship in the lung we demonstrate that the addition of noise results in higher mean tidal volume or lower mean airway pressure. The consequence is enhanced gas exchange or less stress on the lungs, both clinically desirable. Jensen’s Inequality has important considerations in engineering, information theory and thermodynamics. Here is an example of the concept applied to medicine that may have important considerations for the clinical management of critically ill patients. Life support devices, such as mechanical ventilators, are of vital use in critical care units and operating rooms. These devices usually have monotonous output. Improving mechanical ventilators and other life support devices may be as simple as adding noise to their output signals.