  This paper articulates metacognition using the language of statistical
physics and Bayesian mechanics. Metacognitive beliefs, defined as beliefs about
beliefs, find a natural description within this formalism, which allows us to
define the dynamics of 'metacognitive particles', i.e., systems possessing
metacognitive beliefs. We further unpack this typology of metacognitive systems
by distinguishing passive and active metacognitive particles, where active
particles are endowed with the capacity for mental actions that update the
parameters of other beliefs. We provide arguments for the necessity of this
architecture in the emergence of a subjective sense of agency and the
experience of being separate from the environment. The motivation is to pave
the way towards a mathematical and physical understanding of cognition -- and
higher forms thereof -- furthering the study and formalization of cognitive
science in the language of mathematical physics.
