The paper proposes a scenario of origin and emerging of intelligent life in Universe based upon the mathematical discovery of a new class of dynamical systems described by ordinary differential equation (ODE) 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 and quantum-like properties such as randomness, entanglement and probability interference typical for quantum systems have been described. At the same time, these systems expose properties of livings: decomposition into motor and mental dynamics, the capability of self-identification and self-awareness, as well as self-supervision. But the most surprising discovery is the existence of a special sub-class, in which the dynamical systems can violate the second law of thermodynamics, and that makes them different from both Newtonian and quantum physics. This sub-class should be associated with intelligent livings due to capability to move from disorder to order without external help. Based upon the mathematical discovery described above, one can assume that there are good chances that similar dynamical systems representing intelligent livings exist in real physical world. This provides a reason for a ‘rehabilitation’ of the Maxwell demon and put it into physics of intelligent systems. Indeed, the Maxwell demon is implemented by the feedback from the Liouville equation to the original ODE, while this feedback is capable to rearrange the probability distribution against the second law of thermodynamics. In addition to that, the same feedback removes the entropy paradox by explaining high order in our surrounding by ‘intelligent life support’. Two-steps transition: from the Newtonian physics to the linear model of life, and from the latter to the model of intelligent life are analysed. The first transition is triggered by the Hadamard instability of the Newtonian physics with respect to small random disturbances in linear terms of the Liouville feedback. The second transition is triggered by instability of linear model of life with respect to small random disturbances of non-linear terms of Liouville feedback. This transition could be implemented by such physical phenomena as shock waves or negative diffusion in probability space. Both transitions can be associated with catastrophe theory, in which sudden shifts in behaviour arises from small changes in parameters of the model. In view of the proposed model, possible competition between artificial and human intelligence are discussed.