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Non-thermal Brownian motion of a particle in 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 definition of the diffusion coefficients due to non-thermal particle fluctuations: the Einstein relation and the fluctuation theorem. The temperatures from both methods agree well and exhibit a high value of 10 6 K. They depend on the coarsegraining time, which reflects the anomalous properties of the macroscopic fluctuations in the SMT.

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