We introduce a family of Maxwellian Demons for which correlations among information bearing degrees of freedom can be calculated exactly and in compact analytical form. This allows one to precisely determine Demon functional thermodynamic operating regimes, when previous methods either misclassify or simply fail due to approximations they invoke. This reveals that these Demons are more functional than previous candidates. They too behave either as engines, lifting a mass against gravity by extracting energy from a single heat reservoir, or as Landauer erasers, consuming external work to remove information from a sequence of binary symbols by decreasing their individual uncertainty. Going beyond these, our Demon exhibits a new functionality that erases bits not by simply decreasing individual-symbol uncertainty, but by increasing inter-bit correlations (that is, by adding temporal order) while increasing single-symbol uncertainty. In all cases, but especially in the new erasure regime, exactly accounting for informational correlations leads to tight bounds on Demon performance, expressed as a refined Second Law of Thermodynamics that relies on the Kolmogorov-Sinai entropy for dynamical processes and not on changes purely in system configurational entropy, as previously employed. We rigorously derive the refined Second Law under minimal assumptions and so it applies quite broadly---for Demons with and without memory and input sequences that are correlated or not. We note that general Maxwellian Demons readily violate previously proposed, alternative such bounds, while the current bound still holds.

Charged particle velocity-space diffusion in a prescribed one-dimensional turbulent electric field is investigated through numerical trajectories in phase-space and compared against quasi-linear theory (QL), including resonance broadening (RB). A Gaussian spectrum electric field of variable amplitude E is studied in conjunction with two plasma dispersion relations, namely, the Langmuir and ion-acoustic dispersion. A first parameter scan shows that RB effects become significant for a Kubo number K of a few percent. A Kubo number scan shows that diffusion increases as a power law of D∝K3∝E3/2 for large Kubo numbers. Moreover, at large Kubo numbers, transport processes include significant diffusion measured at velocities much higher than the resonant region, where QL and RB predict negligible diffusion. For times much larger than the trapped particle flight time τb and the autocorrelation time τ0, the velocity distribution departs from a Gaussian. Nevertheless, measurements show that the variance increases linearly in time, with a Hurst parameter of H∼0.5, where the diffusion scales as K5/2∝E5/4 and K3/2∝E3/4 for small and large Kubo number, respectively.