I can see a theoretical way it could work - the air enters the wide end, compresses as the bottle narrows, heats up above ambient temperature due to the compression, dumps its excess heat to the plastic of the bottle, and then expands back to ambient pressure as it exits the nozzle thus cooling below ambient temperature - the bottle then radiates away the heat, either mostly outside through virtue of the shape of bottle, or just equally outwards and inwards which still results in some cooling effect.

I find it very hard to believe that you'd have any appreciable compression without gale force winds though. And you don't get to "accumulate" minute amounts of cooling either - the temperature of the "chilled" air coming in is the coldest it will get.

I think you don't need to invoke the heat exchange with the bottle to be relevant. I also believe that you get to accumulate it but there is a negative feedback due to the temperature gradient which prevent you to reach a high temperature difference.

For what it's worth (I'm not a physicist), here is my mental model of how I think it works. We are working at equilibrium we don't care about the macroscopic flow of air as it balances out. When the wind blows in the bottle it creates a more ordered arrangement of the air molecules (imagine laminar or vortex) at the neck (zone of low entropy). The internal energy will diffuse toward the region of more order (Second principle). So internal energy of the inside air flows towards the interface where it then diffuse into the nearby flow and get carried away by the wind.

As soon as there is a temperature difference between the inside air and outside air, traditional heat exchanges also occurs at the interface which has an opposite effect.

This is the claim:

It’s the same as blowing on your hand with your mouth wide open – the air is hot.

Now, when you blow with your lips pursed the air is cool – Eco-Coolers do the same thing.

Which does feel like it works...

Illustration: http://i.dailymail.co.uk/i/pix/2016/06/10/18/3521DBE60000057...

I don't know enough about thermodynamics to judge it but a quick search for "venturi effect heat pump" reveal this patent: http://www.google.com/patents/US20090183858