Why does the nature always prefer low energy and maximum entropy? Why does the nature always prefer low energy and maximum entropy?
I've just learned electrostatics and I still have no idea why like charges repel each other.
http://in.answers.yahoo.com/question/index?qid=20061106060503AAkbIfa
I don't quite understand why U has to be minimum. Can someone explain?
 A: Nature has no preferences, and therefore entropy tends to increase. 
Sounds paradoxical? 
The point is that each microscopic state (describing the exact position and velocity of each atom in the system) is equally likely. However, what we typically observe is not a micro state, but a course-grained description corresponding to incredibly many micro states. Certain macro states correspond to far fewer micro states than other macro states. As nature has no preference for any of these micro states, the latter macro states are far more likely to occur. The evolution to ever more likely macro states (until the most likely macro state, the equilibrium state, is reached) is called the second law of thermodynamics. 
The decrease of potential energy is the consequence of the first (energy conservation) and second (evolution to more likely macro states) law of thermodynamics. As macro states with a lot of energy stored in heat (random thermal motion) contain many more micro states and are therefore much more likely, energy tends to get transferred from potential energy to thermal energy. This is observed as a decrease in potential energy.
A: Firstly I would like to point out that the total energy is actually conserved and can't become greater or lesser. What we are talking about here is the potential energy of the system.
Secondly, I think that this is a really fundamental question and, although very interesting, such questions tend to end up in philosophy. Thirdly I will try my best to give some answers.
Usually minimum potential energy principle is viewed (at least that's the way I see) as a basic principle of the world. You can compare the minimum potential energy principle or electrostatic forces with a force that you maybe know a little bit better:
- Why does gravity make masses attract?
- Because that's the way it is, it's fundamental law of nature.
I don't know if you believe* in gravity, but I do. And I believe in energy minimization aswell.
However, if you want an explanation, it can also be explained by other laws. In this case it's the maximum entropy principle you mentioned (also known as second law of thermodynamics). This law tells that the system will try to maximize it's entropy. The consequence is that all the energy will try to convert into thermal energy (heat) thus increasing the entropy.
Now you run into next question - why maximum entropy? Well, this is once again usually viewed as a basic principle of nature's mechanisms, but it can actually be derived from statistical physics. However, by doing this, you might once again run into some principles of physics and mathematics ad infinitum so in the end you'll have to believe in some principles or at least think in the "if this is correct, then this is what follows:" way. 
-*-  by using the concept of belief I talk about believing a formula or a law without formal proof, but it is proven by experiments that the formula works. Even if a principle is not the principle on which nature bases processes, it surely gives the same results.
A: Well, I'd mention that entropy is significantly more counter intuitive than some may think. In particular since all microstates have equal probability, or in other words are equivalent, if you were to cut your finger off, the state were the chunk comes back into place all by it self if a perfectly valid assumption. There is nothing in this respect that ties this state to a specific energy level. 
Now, to answer the question, why has this never been seen? (And not why is this impossible...). Since our body consists of billions of atoms, you'd need to have them jump back all at once were they came from. As opposed to simply hop around in uncorrelated moves, or in short... Decay.
So, that's the core of the entropy principle. Macro states are the results of billions of different microstates, and we only see an average value.... The most probable one is simply the one that has the largest number of compatible microstates. Hence the chunk is very unlikely to go back to its place on its own. 
Some would say, it is just an artificial way to put it. 
What would be the odds, when assembling dumb atoms, of an intelligent life form? Or in other words how large the sampling experiment should be to witness something else than a dead rock?
:)
A: consider a system of gas particle inside a perfume bottle. Now lets say you spray the gas out, and the system of particle now gets spread all around in a Random manner. Well,now lets see this particles as waves(matter waves) ,just like the electron clouds. I admit, I don't have any deep understanding of quantum mechanics but from what I have learnt from my intermediate chemistry is that more the electron clouds spread, lesser is their energy.   So , when the particles spread uniformly everywhere with maximum entropy, the electron cloud spreads all through out, As such they attain a stable and lower energy state. Now lets come to your next question of lower energy. It isn't so that nature or systems of nature prefer lower energy states, but rather they  can't proceed further when  they have  the lowest possible energy. Like consider a ball thrown up from the ground when it comes down to ground it lacks any more energy or any external force to be back to air.  Now it still remains a mystery to me as to how they can attain this stable state in finite amount of time and can there exist systems which has a stable state but it surpasses it.  So ,this was all my  audacious attempt to explain this tendency of nature with intuitions of quantum mechanics. 
