I will begin from the same argument as Roger above:
Cyanobacteria
These bacteria are useful due to (direct quote courtesy of Roger):
- Carbon fixation. They can pull CO2 out of the endlessly-refreshing atmosphere and convert it to something useful and cumulative.
- Nitrogen fixation. They can also pull N2 out of the atmosphere and give us ammonia and other useful compounds.
- Colonies. They can form sheets, which is useful for helping our body of water stay heterogenous, with a well-lit aerobic zone on top and a dark anaerobic zone at the bottom.
This gives us a good starting point. We have a form of life than is generating basic organics, as well as stratifying the environment into useful layers. This will become important later on. If we assume the "dust" is moderately nutrient rich, we also have an initial biomatter to allow normal reproduction (as even asexual reproduction requires some nutrients to be present).
Over time, this will introduce evolutionary pressures. Ammonia concentration in the water will increase over time, as will the presence of complex organics.
Ammonia and Nitrogen Compounds
The increasing concentration of nitrogen-containing compounds will apply an evolutionary pressure as it builds from harmless to caustic levels. This will also have the effect of slowly increasing the volume of the liquid present, while compressing the "atmosphere". We have assumed that the walls will never budge or burst (and are completely non-porous), and that the atmospheric concentrations are kept uniform. This then is a isochoric process. This implies that atmospheric pressure will increase over time. This will increase the levels of dissolved gasses in the liquid, as well as the overall temperature of the system. This is where the system diverges one of two ways in the short term.
If the device also extracts gasses that aren't "normal", gaseous ammonia, water vapour, and other compounds will slowly leave the system. Let us assume that the device operates at some flow rate K litres per minute (STP). If this flow rate exceeds the rate of nitrogen production and evaporation, the atmosphere will stay approximately earth-like indefinitely. We can call this the well-regulated system. Conversely, if the rate of gas generation and evaporation is greater than the flow rate K, then "seasons" will form. This can be the badly-regulated system.
The well-regulated system
In this scenario, temperature, pressure and atmospheric gasses will all remain at roughly starting levels. This scenario is "less interesting" in that it has lower evolutionary pressure. I will discard this scenario as we are specifically trying to force evolution.
The badly-regulated system
In this scenario, gasses are regulated, but poorly, or not quickly enough. This is the more interesting scenario. Temperature, pressure, and concentration of nitrogen compounds (especially ammonia) will increase until it reaches critical levels and begins killing the cyanobacteria. This will purge any members of the population with low ammonia, pressure, or temperature tolerance, leaving only the strongest members. The purge has two useful effects:
- Evolutionary pressure. The purge ensures only the "fittest" survive.
- Self-regulation. The sudden decrease in bacteria will slow the nitrogen production, and should allow the atmospheric purifier time to re-adjust the atmosphere.
I will designate the less hostile season "summer", and the more hostile season "winter".
The system will start in summer, and the first winter will take a long time. Despite this, it will probably be one of the largest purges in this system. Conditions will become violently hostile in multiple ways, and very few bacteria will survive this. It is also entirely possible that the first winter is a 100% extinction event. In this case, the experiment can be restarted. If we have no way of observing the system, the experiment should be run in parallel to maximise the chance of a successful set.
The survivors of the first winter will form the base population for the second "year". These will be the most chemically and physically resistant of the initial population. Thus, population growth will begin again in a more toxic environment than their predecessors. This will specialise the bacteria with each winter, and encourage mutations that enable survival in the hostile environment, as well as rapid population growth once summer rolls around.
Now that we have a system that encourages mutation, we can begin to answer the question.
If we were to deploy a strain of aquatic bacteria into this
hypothetical room, and waited billions of years, would it be feasible
for things like sexual reproduction, complex multicellularity, and
eventually air-breathing fauna to evolve? The major differences here
from the real world are:
- The confined space
- The lack of change (Same space, same light, same air etc.)
So, do these prohibit the likes of bacteria evolving into as complex
organisms as we see on our Earth? Can extremely complex ecosystems
exist in a 40 m x 35 m x 50 m space? A further clarification: imagine
this room is on Earth, so the gravity will be Earth-like.
Bonus question: could macroscopic flying animals evolve in such a
small, windless, thermal-less place? Feel free to ask more questions
on the conditions of the room if I've left any out.
EDIT: the founding bacteria will be photoautotrophs, and once they
have reached a stable population, heterotrophic ones will be
introduced.
Let's break it down.
Multi-cellular life
It is possible for multi-cellular life to form here. The ocean will eventually be home to many nitrogen-based compounds, and the high pressures of winter may encourage complex molecules to form, including amino acids. Decomposing bacteria will also add biomatter to the equation. This will take many "years". However a "year" here is a summer->winter->summer cycle, not a year as we understand it. The main thing that hinders complex life is that as a being's complexity increases, it's energy efficiency decreases. This provides a practical upper bound for complexity (and size) within our mini-ocean. We could see the evolution of macroscopic life (after all, 1cm^3 is still tiny in the scope of the "world" it lives in), however, it will most like either (de-)nitrifying, or photoautotrophic as light and nitrogen will be the most abundant resources to consume.
Macroscopic fliers
The ability to fly (or jump really far) might be developed, however there are few evolutionary pressures to force this. The system will develop thermal currents and winds as during "autumn" and "spring", but there is little food in the air, and little benefit if a lifeform can fly. However, airborne bacteria that can survive on just ambient moisture and nitrogen gas may well form.
Sexual Reproduction
N.B. This is not my specialty, so I will defer on this point if I am incorrect.
The system I have posited becomes extremely hostile periodically. While sexual reproduction may form, it would not be particularly desirable from my baseline knowledge of evolutionary selection.
Air-breathing Fauna
This one depends on what you mean by fauna and what you mean by air-breathing. A multi-cellular organism that consumes nitrates, and produces nitrogen gas (like a more complex de-nitrifying bacteria) would be perfectly at home in this environment, and it would be "air-breathing". If you mean oxygen-consuming specifically, then it is possible that a fauna may form that is photosynthetic during summer and nitrogen-breathing during winter (when the "sun" is covered by clouds of nitrates). I'm not aware of any physical or chemical limitations that would prevent this from happening, however, the mutation may simply never occur.
Conclusion
It is entirely possible for you to generate complex life and force evolution in a number of interesting ways in your mini-world. However it does require rigging the process a little bit to maximise evolutionary pressure, while not going so harsh as to kill everything. Additionally, the physical bounds of the world (Watts of sunlight, volume, presence and type of atmosphere, nutrient presence and replacement) have to be carefully calibrated to prevent mass extinctions, or failure to evolve at all.