How can we claim that the entropy of the universe is increasing concerning the obvious low entropy of life, solar systems or a galaxy?

The total entropy of the cosmos is increasing.  The increasing order of living systems (a temporary thing) is bought at the expense of more entropy in the rest of cosmos.

The universe is expanding continuously. With the increase in size , the number of available quantum states are also increasing. The entropy is directly related to the natural logarithm of the total available quantum states. So if you believe in the expansion of universe, then you have to believe in the increase of entropy.

I propose two types of entropy: (1) general, and (2) local entropy. When we talk about large unconnected systems such the the air molecules in a room, weather, or the universe itself, then the general or summed up entropy of that system always tends to be increasing as given by the 2nd law of thermodynamics. That is just how nature behaves. However, in the regime of individual cooperative systems that functions as a unit, such as a cell and ultimately life as well as the solar system, then given the right conditions they will have the tendency to decrease entropy locally. Note that the local entropy decreases but still somewhere else outside of that system, the entropy increases. The interesting question is that what is the margin or the division between systems you could refer to as that of general or local? Correct me if my thinking is right but the problem can be regarded as the division between the regime of relativity and quantum mechanics. There is no sharp (quantitative) separation wherein you can tell, "oh, this system is larger that x meters so this falls in the Newtonian or relativistic regime." Our description of nature is not like that way. Instead, depending on the certain physical parameters we look at, we can qualitatively describe its entropy based on that parameter and the answer turns out to be pretty general. In other words, when you look at sufficiently large system with component not necessarily related to each other, then general entropy is always increasing. But when you look at sufficiently specialized system that evolved to function as a unit, then it has the tendency to counter the general entropy increase outside the system and instead decrease the local entropy given 2nd law of thermodynamics is still satisfied. What do you think?

The likely answer is the "Hum" of Universality, which we find manifested in Life, Solar Systems and Galaxies. This "hum" of highly connected self-organisation allows for local pockets of low-entropy order to emerge and evolve over time from the global trend towards high-entropy dis-order. This resonance, energy/work-mimimising, robustness-enhancing, entropy-exporting process has a fractal structure over time; and optimal, analogical, dynamical, geometric signatures and symmetries. https://asynsis.wordpress.com/2014/05/08/the-hum-do-solar-system-orbital-dynamics-display-asynsis-constructal-geometries-and-behaviours/ Order, actually (and seemingly paradoxically), generates more entropy than disorder; thereby better speeding the universe towards thermal (and other) equilibria. It does this within far from equilibrium, dissipative local open systems, which export their entropy into their global environments. Evolving complexity, epitomised by life - is actually a signature of how open systems can lower their internal entropy by exporting it, thereby preserving the 2nd law of thermodynamics. The entire universe itself (if it's part of a larger multiverse), and also if (big conjectural if), like life - if it's an information-processing system, then it might also be somehow exporting its entropy in a way that we don't yet understand (but there are candidate mechanisms). It certainly is importing low entropy in the form of its big bang origins, just as the Gaian earth system imports low entropy from the sun. So in a Copernican context, maybe (very big speculative maybe), the universe too, is a far from equilibrium,  open dissipative structure - in the Ilya Prigogine sense. Such structures exhibit self-organised critical, edge of chaos, universality behaviours, which are reflexive and feedback-led. To re-iterate, they  exhibit self-organised, inferred-predictive and self-observing, recursive processes. So maybe, after A N Whitehead, the universe too is (in a Gaian sense, and in deep-time), analogous to an organism. This proposal is perhaps something that Schrodinger himself would find intriguing - since he was probing universal boundaries at the quantum and thermodynamic limits, with his eponymous equation and essay: "What is Life?" However, as a designer myself, I'll take a rain(maker)-check on any potential teleological implications and stay agnostic on any "intelligent (self)designer" speculations. For what it's worth though, my hunch is that the universe can design itself (or auto-catalyse, like a self-organised critical sandpile avalanche or Game of Life extended-transient glider). It can have its design emerge and evolve, optimally and analogically, just from entropy production and export. Bootstrap theory (where a system can self-organise - or design itself, along with the anthropic and the Heisenberg uncertainty principles on energy-time and negative vrs positive energy - see Lawrence Krauss: A Universe from Nothing), have been evoked as a means for us to understand the universe to have self-designed "ex-nihilo," without a designer, leaving us as the "intelligent designers" of our own neo-platonic ideal forms & models of reality, which we often call the "relationship of relationships - or geometry." Maths is in a sense, the code for those shapes being thrown all around (and inside), us. The golden ratio, Φ, Π, e & i are, I like to think, some of the optimisation and efficiency "heuristic devices" or "numerical constants" that in how they relate - reveal the emergent properties of that design. They're the key operative elements of the code, but that doesn't mean there also has to be a coder; perhaps for self-organisation - there just has to be self-consistency. Maybe the code can write itself because it can also tap into a deep well of probabilities, from quantum coherence & entanglement up to self-organised criticality and universality (as life itself is increasingly seen to do - see coverage of quantum biology, including work by Roger Penrose and Stuart Hameroff). These geometries are implicated in both the leading physiological and network theories of that epitome of life (and our transient, ephemeral defiance of entropy-increase): consciousness, (Phi-IIT & Orch OR), so it's perhaps no surprise that we often also perceive them as aesthetically beautiful. Here's Penrose on these same beautiful, regular, repeating but endlessly creative geometries and their application in one case, to my field of architecture: Penrose also speculates that his & Hameroff's Orch OR quantum consciousness position will have to form an integral part of any overall theory of everything. Tononi's Phi-Integrated Information Theory is more modest, but makes a claim for the golden ratio being the key irreducible maximally-integrable neurone-network firing attractor that generates (and can become a measure of), conscious awareness. https://medium.com/@ASYNSIS/phi-vrs-orch-or-as-above-so-below-6c3a670cf7a7 In fact, some of the geometric signatures and patterns we see in those designs (regardless of the "invent/discover" debate - we've invented a logical system that helps us to predict and describe - or discover, the emergent properties, patterns or laws of nature), show us exactly how these and other various numerical constants recursively relate to grow and evolve complexity in the most optimal and parsimonious way possible. Alan Turing, in his last incomplete work before his tragically early death - was actually looking into how optimal, analogical, irreducible Fibonacci geometries were implicated in animate morphogenesis, specifically - plant phyllotaxis. Fascinatingly, "universal computation" - another Turing concept, seems to be part of this "form-giving" and inherently entropy-exporting process, which arises from a very fundamental, "elementary" level according to theoretical physicist, Garrett Lisi. Note the links in the Asynsis Wordpress post below, Universality as covered in the linked Quanta magazine article appears to be directly related to the above Penrose (& Asynsis) quasi-periodic tessellations and to be a means for quantum information-processing power (computation), analogues to optimally, analogically resonate up to classical scales via optimal fractal, multi-scale modularity and non-local connectivity. http://www.dailymotion.com/video/x2lzjq6_garret-lisi-explains-e8-geometry_tech https://medium.com/@ASYNSIS/asynsis-an-extremely-mean-theory-of-everything-fbb95d5f53d8 https://www.quantamagazine.org/20130205-in-mysterious-pattern-math-and-nature-converge/ More recent work emulates this line, also extending it into (often classical physics-human scaled and thermodynamics-led), evolution in inanimate nature as well. So how does entropy-production and export become associated with complexity, life and concepts of aesthetic and geometrical beauty? Here's two recent TEDx presentations on TED conferences in that regard on the (Asynsis) geometries and (Constructal) thermodynamics involved (and Asynsis-Constructal web presence): http://about.me/asynsis http://constructal.org http://tedxtalks.ted.com/video/Form-follows-flow-%7C-Nigel-Readi;search%3ANigel%20Reading