The Stumbling Block of the Gibbs Entropy: the Reality of the Negative Absolute Temperatures

Anghel, Dragos-Victor

doi:10.1051/epjconf/201610802007

Cited by 8 publications

(8 citation statements)

References 9 publications

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“…The conclusions of the opponents of negative temperature have already been challenged [17][18][19][20][21][22][23][24][25][26][27][28]. We especially endorse the arguments given by Frenkel and Warren [21], although we believe that some issues still need to be clarified.…”

Section: Introductionmentioning

confidence: 79%

Negative temperatures and the definition of entropy

Swendsen

Wang

2016

Physica A: Statistical Mechanics and its Applications

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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.Comment: 10 pages, substantially revised, new references, and a new figur

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Section: Introductionmentioning

confidence: 79%

Negative temperatures and the definition of entropy

Swendsen

Wang

2016

Physica A: Statistical Mechanics and its Applications

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“…A critical difference between the consequences of these definitions pertains to the concept of negative temperatures [9][10][11], which by the Gibbs definition, cannot exist. The advocates of the Gibbs entropy reject negative temperatures, claiming that they are inconsistent with thermodynamic principles [12][13][14][15][16][17][18], while other authors have argued that thermodynamics is consistent with negative temperatures, and a different definition of entropy can give correct thermodynamic predictions when the Gibbs entropy does not [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Comparison of canonical and microcanonical definitions of entropy

Matty

Lancaster

Griffin

et al. 2017

Physica A: Statistical Mechanics and its Applications

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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 between two distinct definitions of the entropy based on the microcanonical ensemble: (1) The Boltzmann entropy, defined by the density of states at a specified energy, and (2) The Gibbs entropy, defined by the sum or integral of the density of states below a specified energy. A critical difference between the consequences of these definitions pertains to the concept of negative temperatures, which by the Gibbs definition cannot exist. In this paper, we call into question the fundamental assumption that the microcanonical ensemble should be used to define the entropy. We base our analysis on a recently proposed canonical definition of the entropy as a function of energy. We investigate the predictions of the Boltzmann, Gibbs, and canonical definitions for a variety of classical and quantum models. Our results support the validity of the concept of negative temperature, but not for all models with a decreasing density of states. We find that only the canonical entropy consistently predicts the correct thermodynamic properties, while microcanonical definitions of entropy, including those of Boltzmann and Gibbs, are correct only for a limited set of models. For models which exhibit a first-order phase transition, we show that the use of the thermodynamic limit, as usually interpreted, can conceal the essential physics. PACS numbers: 05.70.-a, 05.20.-y

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“…Refs. [2,[11][12][13][14][15][16][17][18][19] for a heated discussion), but we shall call it the Boltzmann-Gibbs entropy and write…”

Section: General Methodsmentioning

confidence: 99%

The statistics of mesoscopic systems and the physical interpretation of extensive and non-extensive entropies

Anghel¹,

Parvan²

2018

J. Phys. A: Math. Theor.

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The postulates of thermodynamics were originally formulated for macroscopic systems. They lead to the definition of the entropy, which, for a homogeneous system, is a homogeneous function of order one in the extensive variables and is maximized at equilibrium. We say that the macroscopic systems are extensive and so it is also the entropy. For a mesoscopic system, by definition, the size and the contacts with other systems influence its thermodynamic properties and therefore, if we define an entropy, this cannot be a homogeneous of order one function in the extensive variables.So, mesoscopic systems and their entropies are non-extensive. While for macroscopic systems and homogeneous entropies the equilibrium conditions are clearly defined, it is not so clear how the nonextensive entropies should be applied for the calculation of equilibrium properties of mesoscopic systems-for example it is not clear what is the role played by the boundaries and the contacts between the subsystems. We propose here a general definition of the entropy in the equilibrium state, which is applicable to both, macroscopic and mesoscopic systems. This definition still leaves an apparent ambiguity in the definition of the entropy of a mesoscopic system, but this we recognize as the signature of the anthropomorphic character of the entropy (see Jaynes, Am. J. Phys. 33, 391, 1965).To exemplify our approach, we analyze four formulas for the entropy (two for extensive and two for non-extensive entropies) and calculate the equilibrium (canonical) distribution of probabilities by two methods for each. We show that these methods, although widely used, are not equivalent and one of them is a consequence of our definition of the entropy of a compound system. PACS numbers: 05.; 05.90.+m; 02.50.-r

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The Stumbling Block of the Gibbs Entropy: the Reality of the Negative Absolute Temperatures

Cited by 8 publications

References 9 publications

Negative temperatures and the definition of entropy

Negative temperatures and the definition of entropy

Comparison of canonical and microcanonical definitions of entropy

The statistics of mesoscopic systems and the physical interpretation of extensive and non-extensive entropies

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