How, from a biological point of view, can you explain the phenomenon of a muse when inspiration suddenly comes to you? What hormones does it depend on?

Inspiration is not produced by hormones, but by electromagnetic radiation from the brain.

Brain waves are electromagnetic waves of low intensity emitted by the brain from ~ 1 to 100 Hz. They are successfully recorded with an electroencephalograph. They are grouped by frequencies and indicated by Greek letters:

40 Hz | Gamma waves | Strong mental alertness, including perception, problem solving, fear and awareness

13-40 Hz | Beta Waves | Activity, busy or anxious thinking, active concentration, excitement, cognition

7-13 Hz | Alpha Waves | Relaxation during wakefulness, drowsiness before sleep or after sleep

4-7 Hz | Theta waves | Dreams, deep meditation, REM dreams

<4 Hz | Delta Waves | Deep, dreamless dreams, loss of body sensation

From the list, the alpha -frequency is of interest to you. It is believed that the most creative geniuses, such as Einstein, were constantly in an almost unchanged alpha state.

The brain passively (without dedicated attention) seeks combinations and gives you a successful one into account, suddenness is born due to the lack of main attention on enumerating these combinations