Several implications of well-known fluctuation theorems, on the statistical
properties of the entropy production, are studied using various approaches. We
begin by deriving a tight lower bound on the variance of the entropy production
for a given mean of this random variable. It is shown that the Evans-Searles
fluctuation theorem alone imposes a significant lower bound on the variance
only when the mean entropy production is very small. It is then nonetheless
demonstrated that upon incorporating additional information concerning the
entropy production, this lower bound can be significantly improved, so as to
capture extensivity properties. Another important aspect of the fluctuation
properties of the entropy production is the relationship between the mean and
the variance, on the one hand, and the probability of the event where the
entropy production is negative, on the other hand. Accordingly, we derive upper
and lower bounds on this probability in terms of the mean and the variance.
These bounds are tighter than previous bounds that can be found in the
literature. Moreover, they are tight in the sense that there exist probability
distributions, satisfying the Evans-Searles fluctuation theorem, that achieve
them with equality. Finally, we present a general method for generating a wide
class of inequalities that must be satisfied by the entropy production. We use
this method to derive several new inequalities which go beyond the standard
derivation of the second law.Comment: 14 pages, 1 figure; Submitted to Journal of Statistical Mechanios:
Theory and Experimen