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The term active nematics designates systems in which apolar elongatedparticles spend energy to move randomly along their axis and interact byinelastic collisions in the presence of noise. Starting from a simpleVicsek-style model for active nematics, we derive a mesoscopic theory, completewith effective multiplicative noise terms, using a combination of kinetictheory and It\^o calculus approaches. The stochastic partial differentialequations thus obtained are shown to recover the key terms argued in EPL\textbf{62} (2003) 196 to be at the origin of anomalous number fluctuations andlong-range correlations. Their deterministic part is studied analytically, andis shown to give rise to the long-wavelength instability at onset of nematicorder (see arXiv:1011.5408). The corresponding nonlinear density-segregatedband solution is given in a closed form.

Mesoscopic theory for fluctuating active nematics