Microcanonical entropy for classical systems

Franzosi, Roberto

doi:10.1016/j.physa.2017.12.059

Cited by 9 publications

(23 citation statements)

References 45 publications

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“…It is not out of place to mention that the above given definition has recently been, and to some extent still is controversial, in fact it has been recently argued [ 24 ] that only the Gibbs definition of entropy yields a consistent thermodynamics, whereas this would not be the case of Boltzmann entropy. To the contrary, we have pointed out in References [ 13 , 14 , 25 ] that the Boltzmann definition of entropy actually provides a consistent thermodynamics.…”

Section: Introductionmentioning

confidence: 93%

Geometrical Aspects in the Analysis of Microcanonical Phase-Transitions

Bel-Hadj-Aissa

Gori

Penna

et al. 2020

Entropy

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In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the energy level sets of the Hamiltonian of a system under investigation. In particular, it turns out that peculiar behaviours of thermodynamic observables at a phase transition point are rooted in more fundamental changes of the geometry of the energy level sets in phase space. More specifically, we discuss how microcanonical and geometrical descriptions of phase-transitions are shaped in the special case of φ 4 models with either nearest-neighbours and mean-field interactions.

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Section: Introductionmentioning

confidence: 93%

Geometrical Aspects in the Analysis of Microcanonical Phase-Transitions

Bel-Hadj-Aissa

Gori

Penna

et al. 2020

Entropy

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“…In Ref. [1] we have proved that in the limit of a large number of degrees of freedom, the surface entropy predicts the same results as the Boltzmann entropy, included the possibility to observe negative temperatures. In the present work we show that, on the contrary, in the case of small systems these entropies can be inequivalent.…”

Section: Introductionmentioning

confidence: 78%

“…From a geometric point of view, the temperature derived from the surface entropy has an interesting interpretation: it is the average of the mean curvature of Σ E (the hypersurface H(x) = E) which is a geometric quantity. In fact, in [1] we have shown that in the case of the surface entropy it results…”

Section: Consequences Of the Surface Entropymentioning

confidence: 91%

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A microcanonical entropy correcting finite-size effects in small systems

Franzosi¹

2019

J. Stat. Mech.

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In a recent paper [Franzosi, Physica A 494, 302 (2018)], we have suggested to use of the surface entropy, namely the logarithm of the area of a hypersurface of constant energy in the phase space, as an expression for the thermodynamic microcanonical entropy, in place of the standard definition usually known as Boltzmann entropy. In the present manuscript, we have tested the surface entropy on the Fermi-Pasta-Ulam model for which we have computed the caloric equations that derive from both the Boltzmann entropy and the surface entropy. The results achieved clearly show that in the case of the Boltzmann entropy there is a strong dependence of the caloric equation from the system size, whereas in the case of the surface entropy there is no such dependence. We infer that the issues that one encounters when the Boltzmann entropy is used in the statistical description of small systems could be a clue of a deeper defect of this entropy that derives from its basic definition. Furthermore, we show that the surface entropy is well founded from a mathematical point of view, and we show that it is the only admissible entropy definition, for an isolated and finite system with a given energy, which is consistent with the postulate of equal a-priori probability.

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“…Regarding entropy definition, we have used the Boltzmann entropy instead of Gibbs since we are working in the ensemble with constant energy (i. e. a surface in the phase space). Discussions on this subject of descriptions can be followed through references [17,[22][23][24]. With the parameter values corresponding to the H 2 molecule, figure 1 shows the variation of the entropy S(U) which is a growing function of the internal energy U with an inflection point (dashed line, U c ).…”

Section: The Inflection Point For Entropymentioning

confidence: 99%

Entropy behavior for isolated systems containing bounded and unbounded states: latent heat at the inflection point

Flores¹,

Palma-Chilla²

2020

J. Phys. Commun.

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Systems like the Morse oscillator with potential energies that have a minimum and states that are both bounded and extended are considered in this study in the microcanonical statistical ensemble. In the binding region, the entropy becomes a growing function of the internal energy and has a well-defined inflection point corresponding to a temperature maximum. Consequently, the specific heat supports negative and positive values around this region. Moreover, focusing on this inflection point allows to define the critical energy and temperature, both evaluated analytically and numerically. Specifically, the existence of this point is the signature of a phase transition, and latent heat dynamics occur to accomplish the transition. The conditions established below apply to a large variety of potentials, including molecular ones, and have relevance for physics, chemistry, and engineering sciences. As a specific application, we show that the inflection point for the H 2 molecule occurs at −1.26 [eV]. NomenclatureA Energy parameter defining the potential a -1

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Microcanonical entropy for classical systems

Cited by 9 publications

References 45 publications

Geometrical Aspects in the Analysis of Microcanonical Phase-Transitions

Geometrical Aspects in the Analysis of Microcanonical Phase-Transitions

A microcanonical entropy correcting finite-size effects in small systems

Entropy behavior for isolated systems containing bounded and unbounded states: latent heat at the inflection point

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