Table 3.

Summary of findings. SHO = single harmonic oscillator.

Case	S 1	S 2	S 3	Findings
A 1	SHO	HH thermostat	NH thermostat	For all coupling strengths in case A:
A 2		C1,2 thermostat		1. TK and TC of S1, S2 and S3 are in agreement with each other.
				2. Momentum distribution follows a standard normal distribution
B 1	SHO	HH thermostat	Log thermostat	At low to moderate coupling strengths:
				1. TK and TC of S1, S2 and S3 are different from each other
B 2		C1,2 thermostat		2. Momentum distribution of S3 is not standard normal.
				At larger coupling strengths, Gibbs’ canonical sampling is lost.
C 1	SHO	Log thermostat	Log thermostat	Momentum distribution is not standard normal and temperature control fails