Fluctuation theorem [1] is a result about the entropy rate
production in a non equilibrium stationary state of a dynamical
system.
 
A question recently debated is if the relation predicted by the
theorem for the entropy holds also for the dissipated power of a
thermodynamical system in the non equilibrium stationary state.
 
Be $  pi^W (p;  tau)$ the probability distribution function that the
dissipated power $W$ assume the value $W_  tau$ in the time interval
$  tau$; moreover be $w=  langle W_  tau  rangle$ the mean of $W_  tau$
on the entire temporal history and $p=  frac{W_  tau}{w   tau}$.
 
The limit of the quantity $$f^W (p;  tau)=  frac{1}{w   tau}   ln  left(
  frac{  pi^W (p;  tau)}{  pi^W (-p;  tau)}  right),$$ according to what
suggested by the theorem, would behaviour like :
$$f^W (p;  tau)  sim p$$ in the limit $  tau  rightarrow  infty$.
 
To study the effectiveness of this relation a system with evolution
governed by a Langevin equation with a Ginzburg-Landau free energy
is considered. The system is mantained above the critical
temperature in a non gibbsian stationary state through the
imposition by the extern of a shear flow.
 
The study of the system is presented through the test of ergodicity,
the measure of the time correlation of the stress and results on the
trend of the function $f^W (p;  tau)$ for various $  tau$.