I've been told that many systems possess some residual entropy at absolute zero.

This would seem to disagree with the 3rd Law of Thermodynamics? How can this be explained physically speaking?

I am mildly aware that the 3rd law speaks with respect to a **perfect** system but I've never really understood what is meant by this.

## Best Answer

I think it's not purely an issue of degeneracy, from what I understand a system can have a residual entropy even with a unique ground state. I'm not sure, but I think the way it works is that every system would end up in its lowest-energy ground state at

exactlyabsolute zero, but in practice if we are interested in the behavior as youapproachabsolute zero, some systems may have a large number of possible statescloseto the ground state so that if you lower the temperature and measure energy as a function of temperature, the system may not have enough time to "find" the ground state and spend more time in it than other states as T approaches 0. In this case, if you lowered the temperature over some sufficiently huge span of time it would still be true that the average energy as a function of T would approach the ground state energy as T approached 0, but for a more practical span of time in which you lower the temperature and measure how the energy changes (by measuring the heat capacity, which is the rate of change of internal energy with respect to temperature), the energy maynotapproach the ground state energy on a graph of U vs. T.Here's a discussion of residual entropy from

An Introduction to Thermal Physicsby Daniel Schroeder, p. 94 (note the part I bolded below about needing to 'wait eons' for the system to find the ground state, and the other bolded suggesting thereisa unique lowest-energy ground state for the system he's discussing):