  Stochastic chains represent a wide and key variety of phenomena in many
branches of science within the context of Information Theory and
Thermodynamics. They are typically approached by a sequence of independent
events or by a memoryless Markov process. Here, we demonstrate that when memory
is introduced, the statistics of the system depends on the mechanism by which
objects or symbols are assembled, even in the slow dynamics limit wherein
friction can be neglected. To analyse these systems, we introduce a
sequence-dependent partition function, investigate its properties and compare
it to the standard normalization defined by the statistical physics of
ensembles. Then, we study the behaviour of the entropy and the internal energy
in this intrinsic, directional chains finding that they vary around their
thermally-induced equilibrium analogues due to memory effects. We anticipate
that our results are necessary to interpret configurational order and
information transfer in many molecular systems within Materials Science,
Biophysics, Communication and Engineering.
