This work is inspired by the discovery of a new class of dynamical system described by ordinary differential equations coupled with their Liouville equation. These systems called self-controlled since the role of actuators is played by the probability produced by the Liouville equation. Following the Madelung equation that belongs to this class, non-Newtonian properties such as randomness, entanglement and probability interference typical for quantum systems have been described. Special attention was paid to the capability to violate the second law of thermodynamics, which makes these systems neither Newtonian, nor quantum. It has been shown that self-controlled dynamical systems can be linked to mathematical models of living systems. The discovery of isolated dynamical systems that can decrease entropy in violation of the second law of thermodynamics, and resemblances of these systems to livings suggests that ‘Life’ can slow down the ‘heat death’ of the Universe and that can be associated with the Purpose of Life.
