(updated for 2013)
For actual local thermodynamic equilbrium (not ETE), the following are important to keep in mind:
- Detailed balance: transition rate from j to k = rate from k to j (i.e. no net change in particle distribution)
- LTE is equivalent to ETE when or
- LTE is only an approximation, good under specific conditions.
- Radiation intensity produced is not blackbody illumination as you’d want for true thermodynamic equilibrium.
- Radiation is usually much weaker than the Planck function, which means not all levels are populated.
- LTE assumption does not mean the Saha equation is applicable since radiative processes (not collisions) dominate in many ISM cases where LTE is applicable.