Related papers: Gibbs, Boltzmann, and negative temperatures
This pedagogical comment highlights three misconceptions concerning the usefulness of the concept of negative temperature; being derived from the usual, often termed Boltzmann, definition of entropy. First, both the Boltzmann and Gibbs…
The second Tisza-Callen postulate of equilibrium thermodynamics states that for any system exists a function of the system's extensive parameters, called entropy, defined for all equilibrium states and having the property that the values…
Dunkel and Hilbert, "Consistent thermostatistics forbids negative absolute temperatures," Nature Physics, {\bf 10}, 67 (2014), and Hilbert, H\"anggi, and Dunkel, "Thermodynamic laws in isolated systems," Phys. Rev. E {\bf 90}, 062116 (2014)…
The long standing contrast between Boltzmann's and Gibbs' approach to statistical thermodynamics has been recently rekindled by Dunkel and Hilbert [1], who criticize the notion of negative absolute temperature (NAT), as a misleading…
Small systems consisting of a few particles are increasingly technologically relevant. In such systems, an intense debate in microcanonical statistical mechanics has been about the correctness of Boltzmann's surface entropy versus Gibbs'…
A considerable body of experimental and theoretical work claims the existence of negative absolute temperatures in spin systems and ultra-cold quantum gases. Here, we clarify that such findings can be attributed to the use of a popular yet…
Very recently, the validity of the concept of negative temperature has been challenged by several authors since they consider Boltzmann's entropy (that allows negative temperatures) inconsistent from a mathematical and statistical point of…
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…
In recent papers, several authors have claimed that a definition of the thermodynamic entropy in terms of the logarithm of a volume in phase space, originally suggested by Gibbs, is the only valid definition. Arguing from the Gibbs entropy,…
The notion of negative absolute temperature emerges naturally from Boltzmann's definition of "surface" microcanonical entropy in isolated systems with a bounded energy density. Recently, the well-posedness of such construct has been…
We analyze a gas of noninteracting fermions confined to a one-dimensional harmonic oscillator potential, with the aim of distinguishing between two proposed definitions of the thermodynamic entropy in the microcanonical ensemble, namely the…
For more than 100 years, one of the central concepts in statistical mechanics has been the microcanonical ensemble, which provides a way of calculating the thermodynamic entropy for a specified energy. A controversy has recently emerged…
Despite well over a century of effort, the proper expression for the classical entropy in statistical mechanics remains a subject of debate. The Boltzmann entropy (calculated from a surface in phase space) has been criticized as not being…
In this comment we argue that negative absolute temperatures are a well-established concept for systems with bounded spectra. They are not only consistent with thermodynamics, but are even unavoidable for a consistent description of the…
Although Boltzmann's definition of entropy, and, hence, the existence of negative temperatures, are widely accepted, we will show scenarios which apparently at a first glance are inconsistent with our normal notion of thermodynamics. This…
The limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general the…
Do negative absolute temperatures matter physics and specifically Statistical Physics? We provide evidence that we can certainly answer positively to this vexata quaestio. The great majority of models investigated by statistical mechanics…
For a dynamical system far from equilibrium, one has to deal with empirical probabilities defined through time-averages, and the main problem is then how to formulate an appropriate statistical thermodynamics. The common answer is that the…
General relationship between mean Boltzmann entropy and Gibbs entropy is established. It is found that their difference is equal to fluctuation entropy, which is a Gibbs-like entropy of macroscopic quantities. The ratio of the fluctuation…
The recent experimental realization of exotic matter states in isolated quantum systems and the ensuing controversy about the existence of negative absolute temperatures demand a careful analysis of the conceptual foundations underlying…