JPEG XL supports reversible JPEGs transcoding in ~20% less space, which wouldn't be possible if JPEG was very close to the Shannon entropy limit.

JPEG is lossy though - I'm pretty sure these theorems only really apply to lossless compression, because if you allow lossy compression you can do all kinds of things to different t types of data (pictures being the classic case of permitting pretty lossy compression without much noticeable quality degradation)

Maybe I wasn't clear enough: JPEG -> JPEG XL -> JPEG is not lossy, you get exactly the same bits back, but the JPEG XL file is 20% smaller.

Oh, very interesting. I'll have to look into it.

There's a distinction to be made here, order-0 entropy versus higher order entropy. Order here just means how long a chain of symbols that is considered, where order-0 means just count each symbol at a time, versus eg order-1 where you consider chains of two symbols. Like the other commenter says, JPEGXL can recompress JPEGs losslessly to be around 20% smaller by exploiting higher order patterns (eg via move-to-front, lz77-ish matches, and the MANIAC tree context modeling, versus JPEG's RLE (which is "sort of beyond order-0") combined with Huffman coding (which is order-0))