Local thermal vs local thermodynamic equilbrium? I know that their is a difference between thermal equilibrium and thermodynamic equilibrium. The former only requires no heat transfer whilst the latter also requires mechanical equilibrium, dynamical equilibrium etc.
When looking at the meaning of the term 'local thermodynamic equilibrium' the most common description that I am finding is (see e.g. here):

Local thermodynamic equilibrium is when the medium has a well-defined temperature on a scale much greater then the free mean path of a photon. 

This only mentions temperature, and as such to me seems more like a definition of local thermal equilibrium. So my question is this: How are the two concepts of local thermal and local thermodynamic equilibrium defined and distinguished.
 A: I will provide an answer from an astrophysics point of view, in which the term local thermodynamic equilibrium (LTE) is often used. In astrophysics the distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is not carefully made, because there is rarely if ever a situation in this context in which thermal equilibrium might hold without thermodynamic equilibrium. 
The most common situation in which the presence or absence of LTE is considered is for a star. There is a flow of heat from the interior of a star to its atmosphere at large radii, and the temperature varies as a function of radius. So clearly gas near the atmosphere is not in thermodynamic (or thermal) equilibrium with gas in the core. 
However, models of stellar interiors can be vastly simplified if one recognizes that there is still a local thermodynamic (thermal) equilibrium in the sense that the kinetic distribution of the free electrons, the plasma ionization state, and the radiation field at each radius can all be very well described by a single number, a local temperature $T$. The electron velocities obey a Maxwell-Boltzmann distribution, the ionization state follows from the Saha equation, and the radiation field is described by a Planck function (blackbody), all evaluated for some common $T$. 
As the link you provide explains, this works as long as the mean free path of any particles that might transport heat (e.g. photons, electrons) is very small compared to the length scale over which the temperature is changing. In the atmospheres of stars, where the photon mean free path grows large, LTE in the above sense can break down. However, if the electron mean free path is still small enough, it can helpful to apply an even more limited notion of LTE in which one takes the electron velocities to be in LTE, while acknowledging that the radiation field may depart from a Planck function.
To summarize, LTE is a useful concept to the extent that it simplifies the description of a large system as a collection of local regions each described by a single temperature. The distinction between thermal and thermodynamic equilibrium is rarely needed in the situations in which LTE is a helpful approximation.
