 In response to this objection, Vranas (1998) and Frigg and Werndl (2011) argue that most systems that fail to be ergodic are ‘almost ergodic’ in a specifiable way, and this is good enough. We discuss Vranas’ approach below when discussing Gibbsian SM since that is the context in which he has put forward his suggestion. Werndl and Frigg (2015a, 2015b) offer an alternative definition of Boltzmannian equilibrium and exploit the ergodic decomposition theorem to show that even if a system is not ergodic it will spend most of the time in equilibrium, as envisaged by Boltzmann (roughly the ergodic decomposition theorem says that the phase space of every measure preserving system can be partitioned into parts so that the dynamics is ergodic on each part; for details see Petersen 1983). Frigg (2009) suggested exploiting the fact that almost all Hamiltonian systems are non-integrable, and that these systems have so-called Arnold webs, i.e., large regions of phase space on which the motion of the system is ergodic. Lavis (2005) re-examined the Kac ring model and pointed out that even though the system is not ergodic, it has an ergodic decomposition, which is sufficient to guarantee the approach to equilibrium. He also challenged the assumption, implicit in the above criticism, that providing an explanation for the approach to equilibrium amounts to identifying one (and only one!) property that all systems have in common. In fact, it may be the case that different properties are responsible for the approach to equilibrium in different systems, and there is no reason to rule out such explanations. In sum, the tenor of all these responses is that even though ergodicity simpliciter may not have the resources to explain the approach to equilibrium, somewhat qualified properties do.