Negative temperatures and the definition of entropy

Robert H. Swendsen, Jian-Sheng Wang

Published 2014-10-17Version 1

The concept of negative temperature has recently received renewed interest in the context of debates about the correct definition of the thermodynamic entropy in statistical mechanics. Faced with what they regard as a choice of entropy definitions from among a limited set of options, a number of researchers have identified the thermodynamic entropy with the "volume entropy" suggested by Gibbs, and further concluded that by this definition, negative temperatures violate the principles of thermodynamics. We regard none of the options considered for the entropy by these authors as adequate, and we disagree with their conclusions. We demonstrate that Gibbs' volume entropy is inconsistent with the postulates of thermodynamics for systems with inverted energy distributions, while a definition of entropy based on the probability distributions of observable macroscopic variables does satisfy the postulates of thermodynamics. Our results affirm that negative temperature is a valid concept in thermodynamics.