Negative temperatures and the definition of entropy

Abstract

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. Several researchers have identified the thermodynamic entropy exclusively with the "volume entropy'' suggested by Gibbs, and have further concluded that by this definition, negative temperatures violate the principles of thermodynamics. We disagree with these conclusions. We demonstrate that volume entropy is inconsistent with the postulates of thermodynamics for systems with non-monotonic energy densities, while a definition of entropy based on the probability distributions of macroscopic variables does satisfy the postulates of thermodynamics. Our results confirm that negative temperature is a valid extension of thermodynamics.

10 pages, substantially revised, new references, and a new figure

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Cited by in corpus (23)

• Temperature in and out of equilibrium: a review of concepts, tools and attempts
• Efficiency of a quantum Otto heat engine operating under a reservoir at effective negative temperatures
• Statistical Mechanics of Systems with Negative Temperature
• On the dispute between Boltzmann and Gibbs entropy
• The Gibbs "volume" entropy is incorrect
• In defence of negative temperature
• Phase transitions at high energy vindicate negative microcanonical temperature
• Relation between Boltzmann and Gibbs entropy and example with multinomial distribution
• The thermodynamic entropy of a macroscopic quantum system is a continuous function of energy
• Fluctuation relations and strong inequalities for thermally isolated systems
• Microcanonical entropy for classical systems
• Origin of Negative Temperatures in Systems Interacting with External Fields
• Temperature as a quantum observable
• Critique of the Gibbs volume entropy and its implication
• Multi-temperature atomic ensemble: nonequilibrium evolution after ultrafast electronic excitation
• Negative temperature is cool for cooling
• Resolving the Debate Between Boltzmann and Gibbs Entropy: Relative Energy Window Eliminates Thermodynamic Inconsistencies and Allows Negative Absolute Temperatures
• Resolving the debate about proposed expressions for the classical entropy
• Coarse-graining and symplectic non-squeezing
• Geometrically Frustrated Systems which are as Singles Hotter Than in Company
• Equilibrium and Non-equilibrium Gross-Pitaevskii Lattice Dynamics: Interactions, Disorder, and Thermalization
• The curious case of operators with spectral density increasing as $\Omega (E)\sim e^{Const.E^2}$
• The statistics of mesoscopic systems and the physical interpretation of extensive and non-extensive entropies