  We demonstrate that irreversibility arises from the principle of microscopic
reversibility and the presence of memory in the time evolution of a single copy
of a system driven by a protocol. We introduce microscopic reversibility by
using the concept of protocol- and pathway-dependent thermodynamic function, as
defined in J.R. Arias-Gonzalez, arXiv:1511.08017 [cond-mat.stat-mech], and
memory by using the concept of non-Markovianity, as in J.R. Arias-Gonzalez,
arXiv:1511.06139 [cond-mat.stat-mech]. We define work as the change in free
energy and heat as the change in entropy for micoscopic, individual pathways of
a system subject to a protocol. We find that all non-equilibrium statistics
emerge naturally. In particular, we derive most known fluctuation theorems and
formulate two others. While the conservation of energy is invoked both at the
level of the individual pathway and in ensemble-average processes, the second
law of thermodynamics and the time arrow, which are only fulfilled in
ensemble-average processes, are shown to be consequences of microscopic
reversibility and non-Markovianity.
