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My first thought is to draw a Path with the Pen Tool, then stroke it with the Brush Tool. There doesn't seem to be a way to have Photoshop automatically add a stroke to an open path.
You CAN stroke a closed path (shape) so the loop at the end is relatively easy - use the Ellipse Tool, and give the shape a stroke using the features in the Option Bar.
The curve in the example looks like a perfect arc, so you could drage out a circle holding down the Shift key - stroke it - select and delete the bits you don't want.
I did with shape layers, but it is a bit fiddly removing the unwanted part of the arc doing it that way. You have to select the circle with the Selection tool, then add points with the pen tool in just the right place. Then add sacrificial points that you can delete (with the delete key) which breaks the circle.