Authors: Michael Nastac (University of Oxford), Michael Barnes (University of Oxford), Robert Ewart (University of Oxford), James Juno (Princeton Plasma Physics Laboratory), Alexander Schekochihin (University of Oxford)

We propose a theory of Vlasov-Poisson kinetic plasma turbulence in which the cascaded invariant is not energy, but rather the generalized (negative) entropy $C_2 \propto \int d \mathbf{x} d \mathbf{v} f^2$. As particles ballistically stream and get accelerated by turbulent electric fields, the particle distribution function stretches and folds in position and velocity space, and $C_2$ cascades from large (injection) to small (collisional) phase-space scales. We derive scalings for the wavenumber spectrum of the electric field and $C_2$. The effect of the $\delta f$ fluctuations (small scales) on the equilibrium $f_0$ (large scales) is stochastic heating, viz., non-resonant energization of particles accelerated by the chaotic electric fields. We verify this theory using direct numerical simulations of a 1D-1V plasma and find good agreement. We discuss the implications of our work on the turbulent dissipation and relaxation of particle distribution functions in nearly collisionless space and astrophysical plasmas.