I carry a 15" laptop, headphones, tablet and other misc items in my backpack during the bike ride. This makes me sweaty in the back.
Are there 'breathable' backpacks specifically meant for bike riding that would reduce the sweatiness?
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Nothing works as well as panniers for keeping your back dry, that said, Deuter backpacks have an "AirMesh" that places a mesh wire (laminated) against your back with space between the backpack itself and your back for improved air circulation. It works reasonably well as I used this with a laptop for a few years until I smartened up and went with panniers.
The easiest solution is to get the stuff off your back (put the backpack on a rack/basket or use panniers with a rack).
However, lots of companies make "active backpacks" which are designed to prevent back sweat, usually with some extra spacers or something so that the backpack is not completely in contact with your back, such as this timbuk2 bag.
Messenger bags also work to some extent, since they have lower contact area with your back.
I use this one:
More images here: https://duckduckgo.com/?q=quechua+forclaz+22
It has a breathable back and a special hole for water bag.
I have a MEC Air Hike backpack that I use when I'm on my bike that doesn't have racks. They seem to have changed the design a bit since I bought it. Mine has smaller bumps on the back all over the back. Looks like this new design offers even more breathability. This backpack also has a somewhat stiff back, which I find great for cycling. You can just throw stuff into the pack, and don't have to worry about it jabbing you in the back. The waist belt and chest strap help keep it from flopping around on your back. Mine is also hydration compatible. Too bad they don't appear to sell that model anymore.
Your best chance of relief is a design that features many small pads on the back to help ( as best they can ) keep your back away from the heart of the pack and let some air circulate.
Here are just a few examples, but there are no doubt many more out there: