A nonequilibrium temperature and fluctuation theorem for soft-mode turbulence

Non-thermal Brownian motion of a particle for soft-mode turbulence (SMT) in the electroconvection of a nematic liquid crystal has been experimentally investigated to clarify the statistical and thermodynamical aspects of SMT, using the Lagrangian picture in hydrodynamics. The effective temperature for SMT is obtained in two different ways based on the Einstein relation and the fluctuation theorem from the diffusion due to non-thermal particle fluctuations. The temperatures from the two methods agree well and exhibit a high value of 106 K. They depend on the coarse-graining time, which reflects the anomalous properties of the macroscopic fluctuations for the SMT.