  The joint state of a system that is in contact with an environment is called
lazy, if the entropy rate of the system under any coupling to the environment
is zero. Necessary and sufficient conditions have recently been established for
a state to be lazy [ Phys. Rev. Lett. 106 050403 (2011)], and it was shown that
almost all states of the system and the environment do not have this property [
Phys. Rev. A 81 052318 (2010)]. At first glance, this may lead us to believe
that low entropy rates themselves form an exception, in the sense that most
states are far from being lazy and have high entropy rates. Here, we show that
in fact the opposite is true if the environment is sufficiently large. Almost
all states of the system and the environment are pretty lazy-their entropy
rates are low for any coupling to the environment.
