Turbulent Coronal Heating Mechanisms: Coupling of Dynamics and   Thermodynamics
  Context. Photospheric motions shuffle the footpoints of the strong axial magnetic field that threads coronal loops giving rise to turbulent nonlinear dynamics characterized by the continuous formation and dissipation of field-aligned current sheets where energy is deposited at small-scales and the heating occurs. Previous studies show that current sheets thickness is orders of magnitude smaller than current state of the art observational resolution (~700 km).   Aim. In order to understand coronal heating and interpret correctly observations it is crucial to study the thermodynamics of such a system where energy is deposited at unresolved small-scales.   Methods. Fully compressible three-dimensional magnetohydrodynamic simulations are carried out to understand the thermodynamics of coronal heating in the magnetically confined solar corona.   Results. We show that temperature is highly structured at scales below observational resolution and nonhomogeneously distributed so that only a fraction of the coronal mass and volume gets heated at each time.   Conclusions. This is a multi-thermal system where hotter and cooler plasma strands are found one next to the other also at sub-resolution scales and exhibit a temporal dynamics. 
R. B. Dahlburg, G. Einaudi, A. F. Rappazzo, M. Velli
astro-ph.SR