I speak to the mind body connection a lot in the studio. Physical fitness of any kind is beneficial, but it is important to incorporate one form that requires mental concentration as the source of movement.
The small isometric movements in barre create a kind of active meditation -- you are required to hold the rest of the body quiet while we focus our mind on one muscle to maximize our body's time working it. You can engage a muscle or your core just by thinking about doing so. And that engagement becomes stronger & more pronounced through continued practice.
The feedback I so often get (and feel myself) is that 45 minutes at the barre allows you to shut off your brain. But we're actually doing the opposite. We often feel invigorated and calmed after class and gain a clearer, quieter mind because we just worked out the brain AND the body.
Side benefit? That barre booty.