A fluctuation theorem for phase turbulence of chemical oscillatory waves
  Through numerical simulations of the Kuramoto equation, which displays high-dimensional dissipative chaos, we find a quantity representing the cost for maintenance of a spatially non-uniform structure that appears in the phase turbulence of chemical oscillatory waves. We call this quantity the generalized entropy production and demonstrate that its distribution function possesses a symmetry expressed by a fluctuation theorem. We also report a numerical result which suggests a relation between this generalized entropy production rate and the Kolmogorov-Sinai entropy. 
Shin-ichi Sasa