
Why the earth favors things with lowest energy?
Could you please explain to me? Thank you. 
Question Date: 20141113   Answer 1:
This is an interesting question and really deals
with the most fundamental laws of the universe. A
concrete example of this idea is if you have a
ball that is sitting on a table and you push it
off. Once the ball if no longer on the table, it
can lower its energy by falling to the ground
which will always happen. Though, it’s important
to remember that it’s not the earth that favors
things with the lowest energy, but the entire
universe. Arguably the two most important laws
that govern the universe are the first and
second laws of thermodynamics. The first law
says energy is conserved, which is important to
know, but doesn’t really answer your question. The
answer to your question is a result of the second
law which says that theentropy of the
universe is
always increasing. Entropy is a way to
characterize every system in the universe and can
roughly be thought of a measure of how much you
know about a system before measuring it
explicitly. The simplest example is if you have a
bag of marbles and every marble is red, the system
has an entropy value of zero. If half of the
marbles are red and other half are blue, you have
the maximum entropy value because if you pick a
marble at random, you are the least sure of which
color marble you are going to pick. There are a
number of arguments that can be used to suggest
that the entropy of the universe is always
increasing, but they can be complicated. Everyday
observations like how if you add food dye and
water, they will mix on their own are a
consequence of the second law.
So what does this half to do with energy? Well as
it turns out, energy and entropy are intimately
related. In most any system, if you add energy,
the entropy will increase. Using calculus you can
show that if entropy is at a maximum as is
required by the second law, then energy is at a
minimum. Therefore, energy is minimized in a
system, though it is constant in the entire
universe. In a sense, it’s really the mathematics,
rather than intuition that drive this conclusion.
Though one way to think about it is in the
situation with the ball on a table, what would
happen if the ball didn’t fall down and just
stayed there or floated up? It would probably be
hard for a consistent universe to develop without
energy minimization.
  Answer 2:
That is a good question. The short answer is that
things with the lowest energy are the most
stable. For matter (molecules, minerals, ions,
etc), it is easiest to explain using an analogy:
If you place a ball on a hill it will roll down
the hill to the bottom. If you place a marble on
the side of a bowl, it will also roll to the
bottom. This is because the bottom of the hill,
and the bottom of the bowl are more stable
positions for the ball; the potential energy from
gravity is lower at the bottom. Similarly if you
try to balance a rock on a stick, it will fall
over unless you get it just right, because it is a
less stable position than just lying on the
ground.
For chemistry, the principle is essentially the
same. Chemical reactions happen if the products
are more stable than the reactants, which means
that they have a lower overall energy.
I know that energy is an abstract concept, but I
hope that this helped!
  Answer 3:
This is an interesting question, but let's
rephrase it a little bit: "Why do systems
minimize their energy at equilibrium?" The
answer to this question comes back to the
second law of thermodynamics, which can be
stated in the following way: "The entropy of an
isolated system does not decrease"  that is,
it can only stay the same or increase. It turns
out that a system at equilibrium will maximize
its entropy, which corresponds to a minimization
of energy. Let's think a little more deeply
about what this means and where it comes from.
We can start by thinking about entropy. Entropy is
a measure of the multiplicity of a system, or the
number of "configurations" or "microstates" a
system can access. This is a rather abstract
sentence, so let's use a concrete example to think
about it. Consider a glass of water at room
temperature that is at equilibrium, with a fixed
energy, volume, and number of particles. At any
given time, we can take a picture of the water
molecules and would find that the molecules take
on various positions in the system and
orientations (e.g. which way are the H's
"pointing"). These different configurations in
which we may find the water molecules are the
"microstates" available to the system; there is a
distribution of microstates (each microstate is
accessible with a certain probability), that is
consistent with the macrostate (what we see with
our eyes). Mathematically, we can write the
entropy as:
S = k ln w,
where k is Boltzmann's constant, and w
is the number of microstates. So let's tie
this back into the second law to see why entropy
is maximized at equilibrium. If the entropy of an
isolated system cannot decrease, then the entropy
can only stay the same or increase. At
equilibrium, the entropy is not changing anymore.
In order for the system to have "arrived" at its
equilibrium macrostate, it had to have either
evolved from a system with the same entropy or
lower. This corresponds to having more microstates
possible at this equilibrium macrostate than other
equilibrium macrostates (ln of a large number is
larger than ln of a smaller number). In other
words, the system spends most of its time in
conditions that maximize the number of
microstates, and hence the entropy.
Now, it turns out that maximizing the entropy
corresponds to minimizing the energy. This can be
derived from the first law of thermodynamics, by
starting from the fundamental relationship
:dE = TdS  PdV
(a restatement of the first law) and taking a
second derivative of the whole equation with
respect to some internal degree of freedom. Why a
second derivative? Recall from your calculus
classes that extremum principles come from second
derivatives (if something is concave down, it has
a local maximum and its second derivative is less
than 0 
f"(c) < 0,
vice versa for a local minima). What one finds
when they go through this process is that the
second derivative of S is less than 0 (S" < 0),
corresponding to a local maximum, and the second
derivative of E is greater than 0 (E" > 0),
corresponding to a local minimum.
  Answer 4:
This is a very complicated question. It is really
a question of statistical mechanics, which is a
field of physics and math. I'll try to explain as
best I can.
Nature actually has no preference or favorites,
and this results in systems tending toward the
lowest energy. This sounds like it doesn't make
any sense but I can help explain this with a
simple experiment. First note that energy isn't
ever created or destroyed, it is conserved, so
it has to go somewhere. In reality, it's often
released as heat. So, let's do an experiment to
see how nature shares energy and has no
preferences, but how this results in preferring
the low energy state. You'll need a pencil and
paper, a coin to flip, and dice to roll.
In general there is this idea of each bit of
matter having different "energy states" where it
holds a certain amount of energy. Let's examine
this a bit farther. Say for example we have two
bits of matter and six bits of energy. (Draw this
part out to follow along.) These two bits of
matter share the energy. How do these bits of
energy get divided up though? Completely
randomly. The universe has no preference for where
the energy goes. So, for each bit of energy, toss
a coin. For heads, place the bit of energy in
matter #1. For tails, place it in #2. Do this for
all six bits, and look at what you get. It may not
be perfectly equal sharing of 3 and 3 bits of
energy. Do this several more times and keep track
of the results. The most common result will be an
even split of 3 and 3 just by chance. This is how
nature distributes energy.
Now, think of those same bits of matter. What
would happen if we brought those two into contact
with four more bits of matter and again let the
energy distribute itself randomly? Do this with a
dice. Make six bits of energy, and roll the dice
to determine where each bit ends up for the 6 bits
of matter. If you do this several times, you'll
see that the most common result is that each bit
of matter has one bit of energy. This is a low
energy state compared to the possibility of having
6 energy on a single bit of matter. So even though
there's no preference for having the lowest
energy, by randomly rolling the dice this is the
most common outcome! That's how the world works
and why things tend toward lowest energy. All
random chance drives it, but because of the way
statistics work out, it looks like everything
is "trying" to get to the lowest energy.
This is incredibly advanced physics, and I highly
encourage you to do the tests yourself to see how
this works, and how energy ends up evenly
distributing itself. It makes it a lot clearer and
really helped me. This marching toward even energy
distribution happens trillions of trillions of
trillions of times every second. It is actually
theoretically what keeps time moving forward
instead of backward, since once you have the six
molecules with the evenly distributed six energy
bits, it won't naturally go back to all the energy
being in only two molecules. Pretty cool.
  Answer 5:
The Second Law of Thermodynamics states that
entropy (physical disorder) must increase over
time. The most disorderly form of energy is
heat, and energy cannot be created or destroyed
(that's the First Law of Thermodynamics), so in
order to produce heat, the only way to do that is
to transform energy from other forms into heat.
Lowering the energy state of other things allows
the energy in them to be released to become heat.
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