Coming to living systems, there is no contradiction to the second law just as a fridge allows heat to go from cold (the interior of the fridge) to hot (the kitchen); the fridge is an open system just like the living cell. So life can go on evolving, filtering deleterious mutations via natural selection and exporting the accumulated entropy as long as the environment can provide free energy. But unlike a state of equilibrium (maximum entropy), a state of disequilibrium is highly unstable and natural phenomena are constantly trying to increase the level of entropy to the maximum degree, but there are means to circumvent this natural tendency. Imagine a mixture of air and fuel vapour, such a mixture doesn't have maximum entropy but it would desire to ignite to release heat and increase entropy; such a system is incredibly stable yet incredibly fragile, thus it's an example of a 'metastable' state. Living systems rely on metastable sources of energy for usable energy and take advantage of enzymes and catalysis to circumvent potential obstacles to the release of such energy from inorganic systems.
The question of the origin of the biological information embedded upon DNA and the associated nucleic acids may be described via Shannon's information theory that proposes information as a form of 'negative entropy' while random noise and interference as the disorder itself; so the second law may be reformulated as an increase in entropy and a decrease in the information quantity of a system. But as mentioned, like fridges, living cells are not closed systems and so in principle, the information quantity of a cell can increase if the information present in the environment also increases (the source of biological information is the environment). Thus, processes such as metabolism, reproduction and locomotion which are central to life and continuity are based on the flow of information between the living system and the environment and exothermic heat (body heat) can be thought of as a means of releasing entropy.
But the very origin of information itself is still in question, if it spontaneously appeared one day, that would be tantamount to a reduction of the total entropy of the universe and thus a violation of the second law. So the information must have been there from the very beginning; but the cosmic microwave background (CMB) has an incredibly uniform spectrum which equates to a state of thermodynamic equilibrium, but that's a state of maximum entropy which equates to minimum information. How can that be so if the second law prohibits the total information quantity of the universe to increase with time? Where did the present 'extra' information come from? In other words, if the universe began in maximum entropy (equilibrium), how did it reach its current phase of disequilibrium?
The answer is surprisingly gravity!
If you put gas in a box and leave it there, it will reach a state of equilibrium but gas in interstellar space is subject to gravitational forces and gradually forms stars via accretion that release free energy or negative entropy. So just because the CMB is uniform, it doesn't mean the early universe was in a state of equilibrium. Hence, when the large scale structure of our universe was forming, the gravitational 'clumping' that caused star and galaxy formation resulted in an 'entropy gap' ∆S, a difference between the actual entropy (Sact = Smax + ∆S) and the maximum possible entropy, therefore stars like our sun are trying to fill this gap with their light. Therefore, all sources of negative entropy or free energy can be extrapolated back to the entropy gap that gravity created.