Thermodynamic geometry, phase transitions, and the Widom line

Ruppeiner, George; Sahay, Anurag; Sarkar, Tapobrata; Sengupta, Gautam

doi:10.1103/physreve.86.052103

Cited by 102 publications

(130 citation statements)

References 18 publications

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“…2(d) shows some special features. In addition to the typical region of positive R near the melting line of ice VII, our analysis reveals three more regions with positive R. First, there is a very narrow area on the vapor side of the liquid-vapor coexistence curve in the vicinity of the critical point; see Figure 3 Figure 3(a), and with both fluids we display the Widom lines corresponding to the locations of maximum |R| along lines of constant p [23,24].) This very narrow area of positive R was first identified on the water coexistence curve, and was interpreted as indicating the presence of solid clusters in the vapor, of a type shown schematically in Fig.…”

Section: Resultsmentioning

confidence: 99%

Thermodynamic R-diagrams reveal solid-like fluid states

Ruppeiner

Mausbach

May³

2015

Physics Letters A

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We evaluate the thermodynamic curvature R for fluid argon, hydrogen, carbon dioxide, and water. For these fluids, R is mostly negative, but we also find significant regimes of positive R, which we interpret as indicating solid-like fluid properties. Regimes of positive R are present in all four fluids at very high pressure. Water has, in addition, a narrow slab of positive R in the stable liquid phase near its triple point. Also, water is the only fluid we found having R decrease on cooling into the metastable liquid phase, consistent with a possible second critical point.Keywords: metric geometry of thermodynamics; fluid equations of state; water; thermodynamic curvature; phase transitions and critical points Extracting general information from thermodynamic properties poses a challenge. Which properties to feature depends strongly on the type of system under consideration, the regime of interest, and the broader context of applicable models from statistical mechanics. Very useful for comparison between different systems would be some representation not dependent on such subjective features. In this paper, we propose R-diagrams, based on the thermodynamic curvature R, as such a representation. At a glance, R-diagrams reveal a number of important fluid properties. We key here particularly on locating solid-like properties of fluids, with particular attention to anomalies in liquid water in the vicinity of its triple point.

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Section: Resultsmentioning

confidence: 99%

Thermodynamic R-diagrams reveal solid-like fluid states

Ruppeiner

Mausbach

May³

2015

Physics Letters A

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“…We point out that the same holds in the Riemannian submanifold defined by N = const., which is the case originally analyzed by Ruppeiner [8,[11][12][13][14]. It can readily be verified that Ruppeiner geometry is flat if and only if…”

Section: Flat Hydrostatic Closed Systemsmentioning

confidence: 99%

“…We set out a particular example where the Ricci scalar of Ruppeiner-like metrics (see definition below) is identically zero in a whole Riemannian submanifold of the space of equilibrium states, except for a set of points where the metric becomes degenerate. This counterexample illustrates that, despite the many tests that the aforementioned conjecture has passed [13][14][15], its scope of validity has yet to be properly delimited.…”

Section: Introductionmentioning

confidence: 99%

Geometric Thermodynamics: Black Holes and the Meaning of the Scalar Curvature

García-Ariza

Montesinos

Castillo

2014

Entropy

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In this paper we show that the vanishing of the scalar curvature of Ruppeiner-like metrics does not characterize the ideal gas. Furthermore, we claim through an example that flatness is not a sufficient condition to establish the absence of interactions in the underlying microscopic model of a thermodynamic system, which poses a limitation on the usefulness of Ruppeiner's metric and conjecture. Finally, we address the problem of the choice of coordinates in black hole thermodynamics. We propose an alternative energy representation for Kerr-Newman black holes that mimics fully Weinhold's approach. The corresponding Ruppeiner's metrics become degenerate only at absolute zero and have non-vanishing scalar curvatures.

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“…It coincides conceptually with the so-called Widom line, originally introduced by Stanley and colleagues [11,12] as the locus of the maximum correlation length. As the correlation length is not readily available from macroscopic fluid data, the Widom line is often approximated as the set of states with extrema in the thermodynamic response functions [11,13,14], such as the isobaric specific heat capacity c p [11,[15][16][17], the isothermal compressibility κ T [18,19], or the thermal expansion α p [20]. This analogy is not undisputed.…”

Section: Introductionmentioning

confidence: 99%