Editing Fluctuation theorem (section)

== Second law inequality ==
A simple consequence of the fluctuation theorem given above is that if we carry out an arbitrarily large ensemble of experiments from some initial time t=0, and perform an ensemble average of time averages of the entropy production, then an exact consequence of the FT is that the ensemble average cannot be negative for any value of the averaging time t:
: <math> \left\langle {\overline \Sigma  _t } \right\rangle  \ge 0,\quad \forall t. </math>

This inequality is called the second law inequality.<ref>{{Cite journal|title = Fluctuations Relations for Nonequilibrium Systems|journal = Australian Journal of Chemistry|date = 2004-01-01|pages = 1119–1123|volume = 57|issue = 12|doi = 10.1071/ch04115|first1 = D. J.|last1 = Searles|first2 = D. J.|last2 = Evans}}</ref> This inequality can be proved for systems with time dependent fields of arbitrary magnitude and arbitrary time dependence.

It is important to understand what the second law inequality does not imply.  It does not imply that the ensemble averaged entropy production is non-negative at all times.  This is untrue, as consideration of the entropy production in a viscoelastic fluid subject to a sinusoidal time dependent shear rate shows (e.g., rogue waves).{{clarify|date=June 2009}}{{dubious|date=February 2015}}  In this example the ensemble average of the time integral of the entropy production over one cycle is however nonnegative – as expected from the second law inequality.