States of matter and hydraulics solution
Look at the animation above. We know that gas molecules have a great deal of space between them. However when the gas becomes heated it expands even more. Air trapped in the brake fluid will expand as it absorbs the heat created by the friction of the brake pads. As the paddle is pushed, the expanded air now has a great deal more room to compress. The air is compressed and the hydraulic system takes a while to engage the brakes

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Hot air is compressed before the brakes are engaged