Do sunrises and sunsets look the same in a still image? A question that popped into my head: if I see a picture of the sun close to the horizon, in an unknown place, can I know if it was taken at sunset or sunrise?
Do sunrises and sunsets look the same in a still image? Can one tell them apart?
 A: If you have a sufficiently advanced camera, then you can distinguish a sunrise from a sunset from a still frame. I will assume that the Sun and the horizon are visible.
The Sun is rotating at roughly 2 km/s at the equator.
This rotation imparts Doppler shifts in the light from the Sun, even in a still frame. So with a sufficiently advanced camera which can detect those Doppler shifts (for example, an IFU).
Then you can measure the rotation axis of the Sun. Now, depending on where on Earth you are (latitude and whether this is sunrise or sunset) the rotation axis of the Sun will appear at a different angle relative to the horizon.
So, not only could you theoretically you figure out whether it is sunrise or sunset, but you could also measure the rotation speed of the Sun and your present latitude.
The Sun and the Earth rotate in the same direction (counterclockwise when viewed from above the North Pole). Thus, the top of the Sun relative to the horizon will rotate in the same direction as the observer.
I will use this fact to describe what you would see due to the Sun's rotation:
During sunset, you must be on the side of the Earth moving away from the Sun. From this angle, the top of the Sun (relative to the horizon, not necessarily North!) will appear blueshifted relative to the bottom of the Sun, since the apparent top of the Sun has a velocity towards Earth (same direction as your side of the Earth).
During sunrise, you must be on the side of the Earth moving towards the Sun. From this angle, the top of the Sun will appear redshifted instead.
Side note: I think in a statistical sense you could distinguish between sunrises and sunsets based on effects mentioned in other answers/comments: temperature of the air, stillness of the air, presence of particulates. Statistical meaning you could theoretically do better than a 50/50 guess with a single image, and better if you allow multiple images taken at the same place or with other variables controlled for. So although those answers/comments do not provide a sure way to distinguish sunrise from sunset, I think they suffice to show that the two phenomena are different on some level.
A: Yes, the temperature of the air that the sunlight goes through to reach our eyes would be different.
At sunset the air would be warm, at sunrise it's colder and that causes the light to refract differently.
This website shows more about it

A: I did not perform any calculations, but if the exposure is long enough, one can see a tiny fragment of sun trajectory. In the northern hemisphere the sun moves from left to right, so the fragments of trajectory will look different at sunrise (left bottom to right top) and sunset (left top to right bottom).
EDIT (11/7/2021): Let me add some calculations. The angular size of the Sun is 0.5 degrees. The visible angular velocity of the Sun is 360 degrees per 24 hours, so the Sun moves by 1/10 of its angular size in 12 seconds. So the direction of the Sun's trajectory can be visible in photos at comparable exposure.
