  Information dynamics is an emerging description of information processing in
complex systems which describes systems in terms of intrinsic computation,
identifying computational primitives of information storage and transfer. In
this paper we make a formal analogy between information dynamics and stochastic
thermodynamics which describes the thermal behaviour of small irreversible
systems. As stochastic dynamics is increasingly being utilized to quantify the
thermodynamics associated with the processing of information we suggest such an
analogy is instructive, highlighting that existing thermodynamic quantities can
be described solely in terms of extant information theoretic measures related
to information processing. In this contribution we construct irreversibility
measures in terms of these quantities and relate them to the physical entropy
productions that characterise the behaviour of single and composite systems in
stochastic thermodynamics illustrating them with simple examples. Moreover, we
can apply such a formalism to systems which do not have a bipartite structure.
In particular we demonstrate that, given suitable non-bipartite processes, the
heat flow in a subsystem can still be identified and one requires the present
formalism to recover generalizations of the second law. In these systems
residual irreversibility is associated with neither subsystem and this must be
included in the these generalised second laws. This opens up the possibility of
describing all physical systems in terms of computation allowing us to propose
a framework for discussing the reversibility of systems traditionally out of
scope of stochastic thermodynamics.
