Q:

http://www.physlink.com/Education/AskExperts/ae539.cfm

They say "Entropy is the number of possible arrangements of a system - so a zero entropy means that no possible states can exist at absolute zero. "

- Mike W

They say "Entropy is the number of possible arrangements of a system - so a zero entropy means that no possible states can exist at absolute zero. "

- Mike W

A:

Entropy is not the number of states but (within a constant factor) the logarithm of the number of states. So entropy of zero doesn't mean no states, but rather a single state. The reasons that it's impossible to be sure a system is in the state of lowest energy (i.e. at temperature T=0) are subtle, not something as crude as there not being a state.

They then elaborate: "At absolute zero the internal energy of the system would be zero since temperature is proportional to internal energy." That's entirely false, The proportionality between absolute T and certain categories of energy breaks down for anything that's cold, and isn't even close for anything that's very cold.

Just in case those weren't enough errors, they add, concerning the loss of energy, "This violates Heisenberg's Uncertainty Principle". Actually, the lowest-energy state will, like any other quantum state, obey the HUP. Its zero-point energy is irrelevant to the temperature.

Mike W.

They then elaborate: "At absolute zero the internal energy of the system would be zero since temperature is proportional to internal energy." That's entirely false, The proportionality between absolute T and certain categories of energy breaks down for anything that's cold, and isn't even close for anything that's very cold.

Just in case those weren't enough errors, they add, concerning the loss of energy, "This violates Heisenberg's Uncertainty Principle". Actually, the lowest-energy state will, like any other quantum state, obey the HUP. Its zero-point energy is irrelevant to the temperature.

Mike W.

*(published on 10/18/2011)*