Entropic and enthalpic phase transitions in high energy density nuclear matter
CCompact Stars in the QCD Phase Diagram IV (CSQCD IV)September 26-30, 2014, Prerow, Germany
Entropic and enthalpic phase transitions in highenergy density nuclear matter
Igor Iosilevskiy , Joint Institute for High Temperatures (Russian Academy of Sciences), IzhorskayaStr. 13/2, 125412 Moscow, Russia Moscow Institute of Physics and Technology (State Research University),Dolgoprudny, 141700, Moscow Region, Russia
Features of Gas-Liquid (GL) and Quark-Hadron (QH) phase transitions (PT) indense nuclear matter are under discussion in comparison with their terrestrial coun-terparts, e.g. so-called ”plasma” PT in shock-compressed hydrogen, nitrogen etc.Both, GLPT and QHPT, when being represented in widely accepted temperature –baryonic chemical potential plane, are often considered as similar, i.e. amenable toone-to-one mapping by simple scaling. It is argued that this impression is illusiveand that GLPT and QHPT belong to different classes: GLPT is typical enthalpicPT (Van-der-Waals-like) while QHPT (”deconfinement-driven”) is typical entropicPT. Subdivision of 1st-order fluid-fluid phase transitions into enthalpic and entropicsubclasses was proposed in [arXiv:1403.8053]. Properties of enthalpic and entropicPTs differ significantly. Entropic PT is always internal part of more general and ex-tended thermodynamic anomaly – domains with abnormal (negative) sign for the setof (usually positive) second derivatives of thermodynamic potential, e.g. Gruneizenand thermal expansion and thermal pressure coefficients etc. Negative sign of thesederivatives lead to violation of standard behavior and relative order for many iso-linesin P – V plane, e.g. isotherms, isentropes, shock adiabats etc. Entropic PTs have morecomplicated topology of stable and metastable areas within its two-phase region incomparison with conventional enthalpic PTs. In particular, new additional metastableregion, bounded by new additional spinodal, appears in the case of entropic PT. Allthe features of entropic PTs and accompanying abnormal thermodynamics regionhave transparent geometrical interpretation – multi-layered structure of thermody-namic surfaces for temperature, entropy and internal energy as a pressure–volumefunctions, e.g. T ( P, V ), S ( P, V ) and U ( P, V ).1 a r X i v : . [ nu c l - t h ] J un Introduction
Phase transition (PT) is universal phenomena in many terrestrial and astrophysicalapplications. There are very many variants of hypothetical PTs in ultra-high energyand density matter in interiors of neutron stars (so-called hybrid or quark-hadronstars) [1], in core-collapse supernovae explosions and in products of relativistic ionscollisions in modern super-colliders (LHC, RHIC, FAIR, NICA etc.). Two hypothet-ical 1 st -order phase transitions are the most widely discussed in study of high energydensity matter ( ρ ∼ g/cc): ( i ) – gas-liquid-like phase transition (GLPT) inultra-dense nuclear matter: i.e. in equilibrium (Coulombless) ensemble of protons,neutrons and their bound clusters { p, n, N ( A, Z ) } at T ≤
20 MeV, and ( ii ) – quark-hadron (deconfinement) phase transition (QHPT) at T ≤
200 MeV. (see e.g. [2, 3]).Both, GLPT and QHPT, when being represented in widely accepted T – µ B plane ( µ B – baryonic chemical potential) are often considered as similar, i.e. amenable to one-to-one correspondence with possible transformation into each other by simple scaling(see e.g. figures 1 and 12 in [4]). The main statement of present paper is that thisimpression is illusive and that GLPT and QHPT belong to different classes: GLPT istypical enthalpic (VdW-like) PT, while “deconfinement-driven” QHPT is typical en-tropic PT (see [6] and [7]) like hypothetical ionization- and dissociation-driven phasetransitions in shock-compressed dense hydrogen, nitrogen etc. in megabar pressurerange (see e.g. [5]).It should be noted that the term ”enthalpic” PT is not accepted and not usedpresently. As for the term ”entropy-driven” PT, it is used already in application torather delicate structural PTs (e.g. [8, 9, 10] etc). In present paper the two terms,entropic and enthalpic PTs, are offered as general and universal ones for wide numberof applications (e.g. [5]). Fundamental difference of entropic and enthalpic PTs,defined in this way, are discussed and illustrated below.
GLPT and QHPT look as similar in T – µ B plane (figures 1(a) and 1(b)). It shouldbe noted that unfortunately this type of representation is not revealing for PT anal-ysis. Fundamental difference between GLPT and QHPT could be more evidentlydemonstrated in other variants of phase diagram widely used in electromagnetic plas-mas community (see e.g. [5]). First one is density–temperature ( T – ρ ) diagram. Twothese phase transitions (GLPT and QHPT) are sometimes considered in T – ρ planeas quantitatively, not qualitatively different in their schematic comparison (see e.g.fig. 2 in [12] and slide 2 in [11]). Numerical calculations of phase boundaries for GLPTand QHPT (see fig. 3 and 14 in [4]) demonstrate significant difference in structure of2 a) Gas-liquid phase transition. (b) Quark-hadron phase transition. Figure 1: Visible equivalence of Gas-liquid (GLPT) and Quark-hadron (QHPT) phasetransitions in symmetric nuclear matter in temperature – baryon chemical potentialplane. Figure from [4]. (GLPT – FSUGold model in ensemble { p, n, N ( A, Z ) } , QHPT– SU(3) model)these two boundaries (fig. 2a below [13]).It should be stressed [14] that remarkably similar structure of boundaries fortwo phase transitions are well known in electromagnetic plasmas. For example itis gas-liquid (left) and ionization-driven (right) phase transitions in dense hydrogen(figure 2(b)) (see Figure in [15]). It is almost evident that two gas–liquid-like PTs, from one side, and two “delocalization-driven” PTs (QHPT and PPT), from other side, are similar to each other. Thissimilarity in forms of phase boundaries manifests identity in key physical processes,which rule by phase transformations in both systems in spite of great difference intheir densities and temperatures. When one compress isothermally “vapor” phase(subscript V ) in case of GLPT, he reaches saturation conditions. At this momentthe system “jumps” into “liquid” phase (subscript L ) with decreasing of enthalpy andincreasing of nega-entropy in accordance with equality rule for Gibbs free energy in1 st -order PT: G V = H V − T S V = H L − T S L = G L , (1)∆ G = 0 ⇔ ∆ H = H V − H L = T ( S V − S L ) ≥ . (2)3 a) Liquid-gas and quark-hadron phase transitions (b) Gas-liquid and plasma phase transitions Figure 2: (a): Gas-liquid and quark-hadron phase transitions (GLPT vs. QHPT) insymmetric nuclear matter [4, 13].
Phase boundaries : – saturation, – boiling, –deconfinement, – hadronization, CP – critical points. (b): Gas-liquid and plasmaphase transitions (GLPT vs. PPT) in hydrogen (figure from [15]). Phase boundaries (left to right): GLPT – saturated vapor, boiling liquid, freezing, melting; PPT –pressure ionization; CP – critical points of GLPT and PPTOpposite order of enthalpy and entropy change should be stressed for both “de-localization-driven” phase transitions (QHPT and PPT) in figures 1(a) and 1(b).The both systems, molecular hydrogen (M) and hadronic mixture (H), are ensemblesof bound clusters, composed from “elementary” particles: protons and electrons inthe case of hydrogen and u- and d-quarks in the case of QHPT. The both systemsreaches correspondingly “pressure-deconfinement” or “pressure-ionization” conditionsunder iso– T compression and then jump into deconfinement (Q) or plasma (P) phasescorrespondingly with increasing enthalpy and decreasing nega-entropy (3), which isjust opposite to that in enthalpic PT (2):∆ G P P T = 0 ⇔ ∆ H = H P − H M = T ( S P − S M ) ≥ , (3)∆ G QHP T = 0 ⇔ ∆ H = H Q − H H = T ( S Q − S H ) ≥ . (3 ∗ )Here indexes “M” vs. “P” and “H” vs. “Q” denote “bound” and “non-bound” phases:molecular vs. plasma, and hadron vs. quark phases correspondingly. It is well-known that quark-gluon plasma (QGP) has “much greater number for degrees offreedom” than hadronic phase (see e.g. [2]). It just means much higher entropy of QGP4s. hadronic phase in thermodynamic terms. This opposite order of enthalpy andentropy changes in two discussed above phase transformation (GLPT and QHPT) ismain reason for phase transition classification and terminology accepted and proposedin present paper: namely enthalpic (GLPT) vs. entropic (QHPT and PPT) phasetransitions.It is evident that besides well-known ionization-driven (plasma) PT, there aremany other candidates for being members of entropy transitions class, namely thosePTs, where delocalization of bound complexes is just the ruling mechanism for thosephase transformations. It is e.g. well-known dissociation-driven PT in dense hydro-gen, nitrogen and other molecular gases (e.g. [16, 17] etc.). It is e.g. more exotic polimerization - and depolimerization-driven
PTs in dense nitrogen and possibly othermolecular gases (e.g. [18, 19, 20, 21, 22] etc .). In all these cases basic feature ofentropic (3) and enthalpic (2) PTs (e.g. [23]) leads immediately to opposite sign of P ( T )–dependence at phase coexistence curve in accordance with Clausius – Clapeironrelation. Hence the positive or negative slope of pressure-temperature phase bound-ary – P ( T ) binodal is the key feature for delimiting of both types of PTs, i.e. enthalpicvs. entropic: ∆ H = T ∆ S > ⇒ dPdT ! binodal > , (4)∆ H = T ∆ S < ⇒ dPdT ! binodal < . (5) Exponentially increasing (VdW-like) form of
P–T phase diagram for ordinary GLPTin hydrogen and other substances is well-known. Similar
P–T dependence of GLPTin nuclear matter was calculated many times, e.g. [25, 24, 4] etc. (see Fig. 3 left).In contrast to that
P–T phase diagram of QHPT (Fig. 3 right) is known, but notwidely known ([26, 12, 11]). It was calculated recently in [4]. Both phase transitions,GLPT and QHPT, have opposite P ( T ) behavior in agreement with (4) and (5). Thisfact is not recognized properly as a general phenomenon [6, 7]. vs. entropic phase transitions in pressure–density (pressure–specific volume) plane The most striking difference between entropic vs. enthalpic types of phase transi-tions could be demonstrated in comparison of their
P–V phase diagrams. It shouldbe noted that just this phase diagram is the most important for analysis of many5 a) Gas-liquid phase transition (b) Quark-hadron phase transition
Figure 3: Pressure–temperature phase diagram of gas-liquid (a) and quark-hadron(b) phase transition in symmetric nuclear matter (figs from [4]).dynamic processes in dense plasma: e.g. shock or isentropic compression as well asadiabatic expansion, including anomalous shock rarefaction waves.
P–V phase dia-gram for VdW-like GLPT in ordinary substances is well known. GLPT in symmetricCoulombless nuclear matter has the same structure (see e.g. [25, 24] etc.). In contrastto that the
P–V phase diagram for phase transitions, which are claimed as entropic
PTs (ionization-, dissociation-, polymerization- and depolymerization-driven PTs andmore general – “delocalization-driven” PTs [6]) were not explored properly yet. Inparticular, the
P–V phase diagram for Quark-Hadron phase transition (QHPT) wasnot explored up to date. It is just in process on the base of QHPT calculations in [4].A good example of typical P − V phase diagram for entropic ionization-driven(“plasma”) phase transition (PPT) in xenon is exposed at fig. 4 accepted from [27](see also fig. III.6.11a in [5]). Even more clearly anomalous thermodynamics in thevicinity of two-phase region for entropic PTs is illustrated at fig. 5 (below) for exampleof dissociation-driven phase transition in simplified EOS (SAHA-model) for shock-compressed deuterium (see also fig. 4 in [27]). Several important features of abnormal thermodynamic behavior in two-phase regionof this PPT and in its close vicinity are demonstrated at the fig. 7 from [27] and fig. 86igure 4:
P–V phase dia-gram of hypothetical ionization-driven (“plasma”) phase transi-tion in xenon. Solid lines – cal-culated isotherms for T ≤ T c and T ≥ T c ( T c ≈ T = 11200 K. Shadedarea – two-phase region. C –critical point. Dot-solid lines –estimated parameters of shockadiabats; N – Nellus et al. , F –Fortov et al . (Figure from [27]).from [28]:1. – more than one isotherms come through the critical point of entropic PT in P – V plane projection (see e.g. fig. 5);2. – several isotherms below and above critical isotherm cross each other not onlyin two-phase region (it is obligatory for entropic PT) but in its close one-phasevicinity;3. – many low- T isotherms P ( V ) T and V ( P ) T lay above , at least partially, ofhigh- T isotherms (i.e. at higher P and higher V , correspondingly). Comment : It should be stressed that features (2) and (3) above means abnormal negative sign of thermal pressure and thermal expansion coefficients in discussed areaaround and within the two-phase region of entropic PT. It means that ( ∂P/∂T ) V < ∂V /∂T ) P <
0. It is reasonable to assume that the violation of (ii) and(iii) occurs in isolated P – V area , which is located between the regions with normalthermodynamics { i.e. with positive sign of ( ∂P/∂T ) V and ( ∂V /∂T ) P } .7 .1 Abnormal negativity of cross second derivatives Negativity of two second derivatives ( ∂P/∂T ) V and ( ∂V /∂T ) P is never isolated event.In frames of straightforward thermodynamic technique it proves to be equivalent tosimultaneous negativity for infinite number of other accompanying second derivativesfor thermodynamic potentials. In particular, negativity of ( ∂P/∂T ) V and ( ∂V /∂T ) P combined with the positivity of heat capacities C V and C P (as obligatory conditionsof thermodynamic stability) leads to the negativity for following six cross derivatives:(here U , S and H are internal energy, entropy and enthalpy):( ∂P/∂T ) V ↔ ( ∂P/∂S ) V ↔ ( ∂P/∂U ) V (6) l l l ( ∂V /∂T ) P ↔ ( ∂V /∂S ) P ↔ ( ∂V /∂H ) P (7) l l ( ∂S/∂V ) T ↔ ( − ∂S/∂P ) T (8) l l ( ∂T /∂P ) S ↔ ( − ∂T /∂V ) S (9)1. It should be stressed and clarified that all ten cross derivatives in (6), (7), (8), (9)are positive or negative or equal to zero simultaneously.2. Note that three cross derivatives in (6) and (7) are equivalent to three conven-tional thermodynamic coefficients:(a) – thermodynamic Gruneizen parameter, Gr ≡ V ( ∂P/∂U ) V ,(b) – thermal expansion coefficient, α T ≡ V − ( ∂V /∂T ) P ,(c) – isochoric thermal pressure coefficient, α P ≡ P − ( ∂P/∂T ) V , Comment : Simultaneous positivity or negativity of two cross derivatives: Gruneizenparameter ( Gr ) and thermal expansion coefficient ( α T ) is well known and, forexample, was used for explanation of abnormal properties of shock compressionof nitrogen (see e.g. [18, 19, 31, 22]) and anomalies in shock compression of silica(see [29] and discussion in [30]) Comment : One should be careful with the sign of two above written derivativeswithin the two-phase region of (congruent) entropic phase transition, first onein (7) and last one in (8): i.e. ( ∂V /∂T ) P and ( − ∂S/∂P ) T . Both the derivativestend to infinity (!) within the two-phase region, where isotherms and isobarscoincide. But the “sign” of this infinity is conjugated with the sign of all eight8ther finite derivatives in (6), (7), (8) and (9). It means that the both deriva-tives, ( ∂V /∂T ) P and ( − ∂S/∂P ) T , tend to minus infinity in the case of negative(anomalous) sign of all other finite derivatives in (6), (7), (8) and (9):( ∂V /∂T ) P → −∞ ⇔ ( − ∂S/∂P ) T → −∞ (in two-phase region) . (10) Comment : Negativity of all notified above second cross derivatives leads to importantconsequences in mutual order and behavior of all thermodynamic isolines in P – V plane, i.e. isotherms, isentropes and shock adiabats first of all.1. – Negativity of ( ∂P/∂T ) V leads to abnormal crossing and interweaving of isotherms;2. – Negativity of ( ∂P/∂S ) V leads to abnormal crossing and interweaving of isoen-tropies;3. – It leads also to abnormal relative order of shock adiabats vs. isoentropies andisotherms;4. – Negativity of ( ∂P/∂U ) V leads to abnormal relative order and crossing of shock(Hugoniots) adiabats.It is known that anomalous crossing of Hugoniots adiabats follows from negativ-ity of Gruneizen coefficient (see e.g. [29]). So-called “shock cooling” of nitrogen inreflected shocks [31] could also be explained with assumption of negative Gruneizencoefficient (see e.g. [18, 19, 20]). Thus abnormal negativity of whole group of crossderivatives (6), (7), (8), (9) is of primary importance for the hydrodynamics of adi-abatic flows, e.g. shock compression, isentropic expansion, adiabatic expansion intovacuum, spinodal decomposition etc. All these problems should be discussed sepa-rately [32, 33] (see also [34]). P – V planeand additional metastable section within two-phase region of entropic phase transition One meets anomalous behavior of isotherms within and near the two-phase region ofdiscussed entropic phase transition at sufficiently low temperature, namely:1. – appearance of return-point behavior of metastable part of isotherm in upperspinodal region at low-density branch of isotherm (see e.g. upper end-point at T = 1500 K at fig. 5); 9. – one more third metastable section with positive compressibility (i.e. ( ∂P/∂V ) T <
0) appears within two-phase region of entropic transition in contrast to conven-tional structure of metastable and unstable parts in enthalpic Van-der-Waals-like (gas-liquid) phase transition. This new metastable section lays between twounstable parts of low enough subcritical isotherms within spinodal region ofisotherm (see e.g. T = 1500 K at fig. 5). Features (6.1) and (6.2) are in con-trast to standard behavior of gas-liquid PT, where one unstable part of isothermdivides two metastable parts in ordinary VdW-loop;3. – one more new spinodal (i.e. boundary between metastable and unstable partswithin two-phase region) appears, which bounds this third metastable section .It is the locus of points obeying condition (12), which is opposite to well-knowncondition of standard spinodal for conventional (enthalpic) gas-liquid phasetransition (11):Conventional spinodal (enthalpic PT) ( ∂P/∂V ) T = 0 , (11)New additional spinodal (entropic PT) ( ∂P/∂V ) T = ∞ . (12)4. – in addition to conventional critical point { i.e. the point, where ( ∂P/∂V ) T = 0and ( ∂ P/∂V ) T = 0 } , which is “upper” in T – V plane, and is “lower” in P – V plane, one more new singular point (notation below – NSP ) appears withintwo-phase region of entropic PT at low enough subcritical isotherm. Isother-mal compressibility is equal to zero in this NSP { i.e. ( ∂P/∂V ) T = ∞} incontrast to the ordinary critical point, where isothermal compressibility is in-finite, i.e. ( ∂V /∂P ) T = ∞ ! This new singular point obeys to (12) and closesdiscussed third metastable section of entropic PT from above in T – V plane(upper end-point) and from below in P – V plane (lower end-point). More de-tailed discussions and illustrations of all mentioned above new objects are inprogress [34].Next anomalous features, exposed at fig. 4 and 5, should be emphasized in additionto those mentioned above:5. – spinodal cupola, which is always located inside binodal cupola in the caseof enthalpic VdW-like PT, now located partially outside of binodal area in thecase of entropic PT (fig. 5)6. – spinodal point of rare branch of isotherm (it resembles “overcooled vapor” inVdW phase transition) may have higher density than spinodal point of densebranch of isotherm (which resembles “overheated liquid”) at low enough sub-critical temperature (fig. 5). 10igure 5: P – ρ phase diagram for hypothetical dissociation-driven (entropic) phasetransition in dense deuterium (SAHA-D code [28]). Solid lines – calculated critical( T c ≈ T << T c ) isotherms. Dashed curves at T = 1500K – initial meta- and unstable parts of isotherm. Shaded area – two-phase region; CP – critical point; BP , SP , BP and SP – binodal and spinodal points for rare(1) and dense (2) phases. SP – new additional spinodal (12). Dashed curves at T = 1500 K – two unstable and three metastable parts of initial isotherm. SP – SP –new metastable part of S -PT (Figure from [28]). The region of discussed above abnormal thermodynamics (AT-region) always accom-panies entropic phase transitions. At the same time it could be isolated region withoutany 1 st -order phase transition-like discontinuity. Two variants of the boundary of suchAT-region should be distinguished.1. AT-region coincides with two-phase region of entropic PT so that AT-regionand PT-region have common boundary. This is just the case for so-called non-isostructural phase transitions, i.e. for transitions between phases with prin-cipally different structures, where coexisting phases could not be transformedcontinuously one into another. Well-known examples of non-isostructural PTsare crystal–fluid PT (melting) and polymorphic PTs between phases with dif-ferent crystalline lattices (e.g. bcc-fcc etc .). Great number of examples for suchPTs with (at least partially) decreasing P ( T )-dependence are well known (seee.g. “Generalized phase diagram” at fig. 16 in [35]).2. The boundary of AT-region (at least partially) located in the region of regular11hermodynamics with continuous transition from area with normal thermody-namics (positive sign of all cross derivatives (6), (7), (8) and (9)) to area withabnormal thermodynamics (negative sign of these derivatives). It is so in par-ticular for the case of isolated AT-region (without phase transition at all) andin the case of isostructural PT, like all fluid-fluid phase transitions, where crit-ical point (or even several critical points!) must exist. New thermodynamicobject appears in this latter case – the locus of points where all cross deriva-tives (6), (7), (8) and (9) are equal to zero simultaneously . (Having no widelyaccepted title for this object we would use below the notation “Zero-Boundary”– ZB). Remarkable features in behavior of thermodynamic iso-lines upon and inthe vicinity of ZB, as well as main consequences for zero-value of cross deriva-tives (6), (7), (8), (9) for main hydrodynamic properties of adiabatic processes,e.g. shock and isentropic compression and expansion etc., will be later discussedseparately.3. The most evident thermodynamic properties at any point of Zero-Boundary arefollowing:(a) Isobaric and isochoric heat capacities are equal to each other: C p ≡ ( ∂H/∂T ) P = ( ∂U/∂T ) V ≡ C V . (13)(b) Isothermal and isentropic speeds of sound are equal to each other: a S ≡ ( ∂P/∂ρ ) / S = ( ∂P/∂ρ ) / T ≡ a T (14)(c) The slopes of four iso-lines: e.g. iso- T , iso- S , iso- U , iso- H (temperature,entropy, internal energy and enthalpy) and slope of shock adiabat (Hugo-niot) in P – V -plane are equal to each other at Zero-boundary:( ∂P/∂V ) T = ( ∂P/∂V ) S = ( ∂P/∂V ) U = ( ∂P/∂V ) H = ( ∂P/∂V ) Hug . (15) X ( P, V ) in the region of abnormal thermo-dynamics All mentioned above anomalies have clear geometric interpretation: – temperature,entropy and internal energy surfaces as a functions of pressure and density, e.g. T ( P, V ), S ( P, V ) and U ( P, V ), have multi-layered structure over the region of anoma-lous thermodynamics in P – V plane in the case of all entropic phase transitions. Itis valid in particular, for all discussed above “delocalization-driven” phase transitions12ike ionization-, dissociation-, depolymerization-driven PTs, as well as for quark-hadron transition (QHPT) etc . Again, one should distinguish two variant of suchmulti-layered structure of T , S and U over P – V plane: ( i ) – when AT-region coin-cides with two-phase region of a phase transition, so that both have the same commonboundary, which is the locus of break in T , S , U -surfaces; and ( ii ) – when AT-regionrestricted (at least partially) by the separate boundary (outside of the two-phaseboundary itself) with zero value for all cross derivatives mentioned in eq-s (6), (7), (8)and (9) (i.e. “Zero-boundary”). Keeping in mind discussed above difference between enthalpic and entropic phasetransitions we ought to summarize main features, which should be classified, whenone meets unexplored phase transition (see e.g. [5, 37]): • Is this PT of 1 st or 2 nd -order? • Is this PT enthalpic or entropic? (this paper) • Is this PT isostructural or non-isostructural (like, for example, gas-liquid PT vs . crystal-fluid PT)? • Is this PT congruent or non-congruent (see e.g. [36, 37, 4])? • Do we use Coulombless approximation in description of this PT (see e.g. [4]),or we take into account all consequences of long-range nature of Coulomb in-teraction? • What is the scenario of equilibrium phase transformation in two-phase region?Is it macro- or mesoscopic one (e.g. “structured mixed phase (SMP)” scenario(or so-called “pasta-plasma”))?In this paper we made accent on analysis of following combination: 1 st -order,entropic, congruent, isostructural and/or non-isostructural, Coulomb-included phasetransitions without possibility of SMP (pasta) scenario. Phase transitions with othermore complicated combination of basic features would be discussed in following pa-pers. Conclusions • Widely accepted visible equivalence of gas-liquid-like and quark-hadron (decon-finement) phase transitions in high energy density nuclear matter is illusive.13
Both phase transitions belong to fundamentally different sub-classes: gas-liquidPT is enthalpic one, while quark-hadron PT is entropic one. • Properties of entropic and enthalpic PTs differ significantly from each other. • Pressure-temperature dependence of phase boundary for enthalpic phase transi-tion ( H -PT) and entropic one ( S -PT) have different sign i.e. ( dP/dT ) H − P T ≥ vs. ( dP/dT ) S − P T ≤ • Isotherms of entropic PT have anomalous behavior within the two-phase regionat sufficiently low subcritical temperature. There is abnormal order for sequenceof stable, metastable and unstable parts: e.g. stable-I / metastable-I / unstable-I / metastable -III / unstable-II / metastable-II / stable-II. • Binodals and spinodals of entropic PT have anomalous order in P – V plane.Isothermal spinodal [e.g. ( ∂P/∂V ) T = 0] may be located outside binodal ofentropic PT at low enough subcritical temperature. • Two-phase region and its close vicinity for entropic PT obey to abnormal ther-modynamics. Namely: negative Gruneizen parameter, negative thermal andentropic pressure coefficients, negative thermal expansion coefficient etc . Be-sides there are anomalous order and intersections of isotherms, isentropes andabnormal order and intersections of shock adiabats (Hugoniots) etc . • All the features of discussed entropic phase transitions and accompanying ab-normal thermodynamics region have transparent geometrical interpretation –multi-layered structure of thermodynamic surfaces for temperature, entropyand internal energy as a pressure–volume functions, e.g. T ( P, V ), S ( P, V ) and U ( P, V ). • Deconfinement-driven (QHPT) and ionization-driven “plasma” phase transi-tions (PPT) as well as dissociation- and depolymerization-driven PTs in N etc .are entropic PTs, and hence they have many common features in spite of manyorder difference in density and temperature. • It is promising to investigate entropic PTs experimentally, for example via vol-umetric heating by heavy ion beams (HIB), in strong shock compression andsubsequent isentropic expansion, in quasi-isobaric expansion with exploding foiltechnique and via surface laser heating etc . • It is especially promising also to investigate entropic PTs theoretically in framesof traditional thermodynamic models (chemical picture) and via ab initio ap-proaches. 14 cknowledgement
We express our thanks to the organizers of the CSQCD IV conference for providingan excellent atmosphere which was the basis for inspiring discussions with all par-ticipants. We have greatly benefitted from this. Author acknowledges V. Gryaznovfor collaboration and for skilful calculations in obtaining phase diagram of model-ing dissociative phase transition in deuterium, and M. Hempell and V. Dexheimerfor collaboration and permission to use joint density-temperature phase diagram forGLPT and QHPT. Author acknowledges also V. Fortov, D. Blaschke and J. Randrupfor helpful and fruitful discussions. This work was supported by the Presidium RASScientific Program “Physics of extreme states of matter”
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