Brownian velocity fluctuations in liquids have fractal dimension 7/4 due to non-Markovian hydrodynamic thermal noise, establishing a new non-equilibrium universality class.
In the Einstein-Langevin approach, the dynamics are Markovian and the particle’s velocity is a stochastic pro- cess possessing the fractal dimension dv = 3 / 2
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The fractal dimension of Brownian dynamics in liquids
Brownian velocity fluctuations in liquids have fractal dimension 7/4 due to non-Markovian hydrodynamic thermal noise, establishing a new non-equilibrium universality class.