Evolution and the arrow of time I don't want to ask about potential resolutions to the arrow of time. On the contrary, I want to take it as a given that it is the case for the universe, but then ask a rather odd question about its applicability (or lack thereof) to the surface of the earth.
The surface of the earth is certainly not a closed system, in that it receives tremendous energy from the sun. For that reason alone, there is no reason to believe its entropy should increase over time. Shouldn't I be able to conclude that, for processes that are only sensitive to conditions on the surface of the earth, there is no arrow of time ? Shouldn't be this be the case for life as a whole ? If I were studying large scale structure formation in the universe, it would make sense to keep in mind that there will be an asymmetry in the change in entropy between one direction and another given the low entropy of the initial conditions. The evolution of life clearly also follows this asymmetry in that if I were to ask in what direction of time I would have to go to find the common ancestor of 2 animals, it would be the same as the low entropy direction of the universe, but there's no clear reason why that should be the case (in other words, if I were to reconstruct the tree of life, there would be a direction from which branches can flow out of points, but never into them). The bacteria floating around a puddle of water are hardly sensitive to the entropy conditions of the whole universe, and only care about their immediate surroundings. More generally, as I've pointed out, there is no reason to think that the surface of the earth will have greater entropy in a billion years. So why can't life appear in the future, and evolve "backwards" relative to us, leading to a separate time reversed tree of life from us ? Why isn't there a second tree of life that sees time "backwards" relative to us, with living beings that seem to multiply "backwards" in time ?
More generally, if this cannot be the case for the surface of the earth if the energy from the sun simply isn't enough to accomplish it, can there exist local systems whose arrow of time will be the opposite of the global arrow of time ?
 A: 
The surface of the earth is certainly not a closed system, in that it receives tremendous energy from the sun. For that reason alone, there is no reason to believe its entropy should increase over time.

We don't say that a puddle's water level must always increase because there's water flowing into it. If there are inflows as well as outflows, we must look to something else to get a sense of where the balance should lie. In the case of the Earth's biosphere energy balance, this is dictated by radiative heat transfer. We receive energy from the sun, and we radiate energy out to space. This forms a very specific radiative physics problem, for which known physics accurately predicts the temperature.
The inflow of energy (as sunlight) is relatively constant. The outflow is dictated by thermal radiation into space, and that's dictated by fairly constant parameters, so it's not surprising that Earth's temperature is relatively constant. That is, unless its albedo changes for some reason, like some mammalian species inducing combustion reactions with geologic hydrocarbon reserves, which causes a sharp change in average absorption spectrum of the atmosphere around those thermal energies.
As the temperature and matter content of the biosphere stays relatively constant, so does its entropy. "Life on Earth" is a collection of events enabled by a flow of energy from one reserve into another.

The evolution of life clearly also follows this asymmetry in that if I were to ask in what direction of time I would have to go to find the common ancestor of 2 animals, it would be the same as the low entropy direction of the universe, but there's no clear reason why that should be the case.

Physically, we must explain why history exists. The most major problem is that laws of physics are generally reversible in time. That means that in the equations we can't tell the past from the future. Our answer to this is incomplete, but it's still pretty good. The point of the big bang itself had extremely low entropy, if not the lowest possible entropy. So obviously entropy increases in one direction, otherwise known as the future. The details are worked out in thermodynamics.
Evolution doesn't modify this challenge unless some argument can be presented which demands more than proving that history exists. There's no fruitful approach within your argument to do this. Common ancestors are just a component of history. So are long-since extinct species.
We can (and do) reformulate physics to the specific subsystem of the universe which is the biosphere. There is abundant low-entropy energy flowing in from the sun, and the energy is released through thermal radiation. In-between those two points energy might get stored, it might be used in an ATP molecule, it might be used once, and then get recycled and used again, it might be used mechanically by some animal, and then dissipated as heat. After the energy is dissipated as heat, it's only a matter of time before that energy leaves Earth through thermal radiation into space.
That radiation is very high-entropy, and does formally contain all the information about everything that's ever happened on (and inside) Earth. Practically we will never recover this information, but the physical argument about balance of energy and the level of disorder of that energy should be perfectly clear. This doesn't have anything to do with evolution, except that it allows for evolution to exist. We never required anything more.
A: The solution to this problem involves considering the physics of information processing. Life involves information processing in at least two distinct ways. 
First evolution can be considered a form of information processing. Mutation produces variations among genes. Some of the variants spread in a particular environment, others do not. Over time the population of genes changes in such a way as to incorporate the sort of information that affects whether a gene manages to copy itself or not in that environment. Second, an individual organism may have sensors that monitor the environment and enable it to respond to some ways in which the environment can change.
And life in general involves doing logically irreversible information processing, and this has a cost in terms of increase of entropy. Evolution throws away any variant of a gene that does not manage to propagate. Organisms throw away some of the information their sensors take in. Organisms do things like kill sensescent cells, i.e. - they throw away the information in those cells. The reading of DNA is also not thermodynamically reversible, see
http://www.pitt.edu/~jdnorton/lectures/Rotman_Summer_School_2013/thermo_computing_docs/Bennett_1982.pdf.
A: In fact, I think that the production of life is actually an example of large-scale order emerging from a more homogeneous state, so evolution in general is probably an example of reduction of entropy of "the system," whatever that's defined as (made possible by the increased entropy of the rest of the universe, since as you say the biosphere is not an isolated system).
As for why the process couldn't happen in both directions in time, I don't think there's any thermodynamic reason in principle that you couldn't have a sort of backwards evolution.  In fact, I think it happens.  You could think, for example, of the fact that current homo sapiens includes genes of neanderthal and cro magnon and probably other early hominids.  If you were to look at the tree of life, we would have connections backwards to multiple sub-species.  Another example might be to consider organisms that rely on simbiotic unions with each other; in a sense, they have merged into a single organism, but their lineages diverge if you trace them backwards (in conventional time).
More generally, though, if you want to think of the change of entropy of a system that is localized (in time and space), I think it's useful to remember that entropy is just a measure of the number of microstates corresponding to a given macrostate.  Increasing entropy just means moving towards a state with more available microstates, which becomes more and more probable the larger the number of microstates becomes.  It doesn't necessarily depend on the entropy of the universe as a whole, or on the fact that the universe began in a low-entropy state.
A: In my opinion there is a misunderstanding here in what the arrow of time means, entropy  and what time is.
Time is a way to measure changes in space:dx/dt ,dy/dt , dz/dt. Take a contour map. If there were no time, the contour is invariant. In a similar way that if there were no dx/dy, dy/dz,dz/dx ...  three dimensional space would be an unchanging invariant volume, no contours, the changes in observed contours force towards a definition of time. Some contours give changes that are used as clocks, to measure time, beginning from the night/day clock to the year clock, to the atomic clock
In our physical theories, in the same way we define (x,y,z) we define t to measure time.
Experimentally, by observations, in contrast to the space dimensions, time only increases. This has been embedded in our theories, and an elegant way of defining time has been by the use of entropy, that entropy always increases or stays the same in closed systems.
There can be subsystems that have decreasing entropy, the balance taken by the rest of the whole closed system. Example: crystal formation from a liquid phase. Another example is living organism from a soup of sustainance, (energy is some form); the whole system has increasing entropy, the living  organism continually decreases its entropy the balance being taken by the environment.
One can define an arrow of time on any physical body, even one which starts with low entropy, as a crystal. Take a crystal and set it in a vacuum . It will be radiating black body radiation, i.e. it will be increasing the original value of entropy for "crystal + radiation"
