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We present a study of energy density and pressure of a free real scalar quantum field after its decoupling from a thermal bath in the spatially flat Friedman-Lemaitre-Robertson-Walker space-time by solving the Klein-Gordon equation both analytically and numerically for different predetermined scale factor functions $a(t)$. The energy density and pressure, defined by subtracting the vacuum expectation values at the decoupling time, feature corrections with respect to the classical free-streaming solution of the relativistic Boltzmann equation. We show that if the expansion rate is comparable or larger than $mc^2/\hbar$ or $KT_0/\hbar$ where $m$ is the mass and $T_0$ the decoupling temperature, both energy density and pressure gets strong quantum corrections which substantially modify their classical dependence on the scale factor $a(t)$ and drive pressure to large negative values. For a minimally coupled field with a very low mass in an expanding de Sitter universe quantum corrections are dominant driving pressure and energy density to become asymptotically constant with an equation of state $p/\varepsilon \simeq -1$, thereby mimicking a cosmological constant. For a minimally coupled massless field, quantum corrections are asymptotically dominant for any accelerated expansion., Comment: 28 pages, 15 figures

Hot QCD physics studies the nuclear strong force under extreme temperature and densities. Experimentally these conditions are achieved via high-energy collisions of heavy ions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). In the past decade, a unique and substantial suite of data was collected at RHIC and the LHC, probing hydrodynamics at the nucleon scale, the temperature dependence of the transport properties of quark-gluon plasma, the phase diagram of nuclear matter, the interaction of quarks and gluons at different scales and much more. This document, as part of the 2023 nuclear science long range planning process, was written to review the progress in hot QCD since the 2015 Long Range Plan for Nuclear Science, as well as highlight the realization of previous recommendations, and present opportunities for the next decade, building on the accomplishments and investments made in theoretical developments and the construction of new detectors. Furthermore, this document provides additional context to support the recommendations voted on at the Joint Hot and Cold QCD Town Hall Meeting, which are reported in a separate document., Comment: 190 pages, 69 figures

We calculate the energy density and pressure of a scalar field after its decoupling from a thermal bath in the spatially flat Friedman-Lema\^itre-Robertson-Walker space-time, within the framework of quantum statistical mechanics. By using the density operator determined by the condition of local thermodynamic equilibrium, we calculate the mean value of the stress-energy tensor of a real scalar field by subtracting the vacuum expectation value at the time of the decoupling. The obtained expressions of energy density and pressure involve corrections with respect to the classical free-streaming solution of the relativistic Boltzmann equation, which may become relevant even at long times., Comment: 18 pages, 1 figure; finally published version

Exergy is a very important thermodynamic quantity in several fields such as economy, engineering, ecology and yet it has attracted little attention in pure physics. One of the main problems of the currently used definition of exergy is its dependence on an arbitrarily chosen reference state, which is the thermodynamic state of a reservoir the system is supposedly in contact with. In this paper, starting from a very general definition of exergy, a formula is derived for the exergy balance of a general open continuous medium without any reference to an external environment. A formula is also derived for the most suitable thermodynamic parameters of the Earth atmosphere when seen as an external environment in the usual exergy applications., Comment: 18 pages, 4 figures. Revised version published in Phys Rev E

The spin polarization measurements of particles emitted in heavy-ion collisions have opened the possibility for new phenomenological investigations of spin physics in relativistic fluids. The theoretical predictions of global polarization are in agreement with the data, but consistent discrepancies stand out for the local polarization. We show that the covariant theory of relativistic quantum fluids at local equilibrium implies an additional, non-dissipative contribution to the spin polarization vector, which is proportional to the thermal shear, which has been previously overlooked. This additional contribution, together with an improved approximation in the expansion of the local equilibrium density operator, restores the quantitative agreement between the theoretical predictions and the experimental data., Comment: 6 pages, 2 figures, presented at the XXIXth International Conference on Ultra-relativistic Nucleus-Nucleus Collisions (Quark Matter 2022). v2: Added ancillary files for the figures

Since the first evidence of a global polarization of $\Lambda$ hyperons in relativistic nuclear collisions in 2017, spin has opened a new window in the field, both at experimental and theoretical level, and an exciting perspective. The current state of the field is reviewed with regard to the theoretical understanding of the data, reporting on the most recent achievements and envisioning possible developments. The intriguing connections of spin physics in relativistic matter with fundamental questions in quantum field theory and applications in the non-relativistic domain are discussed., Comment: 16 pages, published in Reports on Progress in Physics

We show that the inclusion of a recently found additional term of the spin polarization vector at local equilibrium which is linear in the symmetrized gradients of the velocity field, and the assumption of hadron production at constant temperature restore the quantitative agreement between hydrodynamic model predictions and local polarization measurements in relativistic heavy ion collisions at $\sqrt{s_{\rm NN}} = 200$ GeV. The longitudinal component of the spin polarization vector turns out to be very sensitive to the temperature value, with a good fit around 155 MeV. The implications of this finding are discussed., Comment: 6 pages, 6 figures. Version accepted for publication in Phys.Rev.Lett

We show that spin polarization of a fermion in a relativistic fluid at local thermodynamic equilibrium can be generated by the symmetric derivative of the four-temperature vector, defined as thermal shear. As a consequence, besides vorticity, acceleration and temperature gradient, also the shear tensor contributes to the polarization of particles in a fluid. This contribution to the spin polarization vector, which is entirely non-dissipative, adds to the well known term proportional to thermal vorticity and may thus have important consequences for the solution of the local polarization puzzles observed in relativistic heavy ion collisions., Comment: 10 pages, 1 figure; version accepted for publication in Physics Letters B

We study a relativistic fluid with longitudinal boost invariance in a quantum-statistical framework as an example of a solvable non-equilibrium problem. For the free quantum field, we calculate the exact form of the expectation values of the stress-energy tensor and the entropy current. For the stress-energy tensor, we find that a finite value can be obtained only by subtracting the vacuum of the density operator at some fixed proper time \tau_0. As a consequence, the stress-energy tensor acquires non-trivial quantum corrections to the classical free-streaming form., Comment: 19 pages, 1 figure

We show that local parity violation due to chirality imbalance in relativistic nuclear collisions can be revealed by measuring the projection of the polarization vector onto the momentum, i.e. the helicity, of final state baryons. The proposed method does not require a coupling to the electromagnetic field, like in the Chiral Magnetic Effect. By using linear response theory, we show that, in the presence of a chiral imbalance, the spin 1/2 baryons and anti-baryons receive an additional contribution to the polarization along their momentum and proportional to the axial chemical potential. The additional, parity-breaking, contribution to helicity can be detected by studying helicity-helicity azimuthal angular correlation., Comment: 13 pages, 3 figures; final version to appear in Physics Letters B

We derive a general exact form of the phase space distribution function and the thermal expectation values of local operators for the free quantum scalar field at equilibrium with rotation and acceleration in flat space-time without solving field equations in curvilinear coordinates. After factorizing the density operator with group theoretical methods, we obtain the exact form of the phase space distribution function as a formal series in thermal vorticity through an iterative method and we calculate thermal expectation values by means of analytic continuation techniques. We separately discuss the cases of pure rotation and pure acceleration and derive analytic results for the stress-energy tensor of the massless field. The expressions found agree with the exact analytic solutions obtained by solving the field equation in suitable curvilinear coordinates for the two cases at stake and already - or implicitly - known in literature. In order to extract finite values for the pure acceleration case we introduce the concept of analytic distillation of a complex function. For the massless field, the obtained expressions of the currents are polynomials in the acceleration/temperature ratios which vanish at $2\pi$, in full accordance with the Unruh effect., Comment: 38 pages, 1 figure. Final proofread version published in JHEP

We review the calculation of polarization in a relativistic fluid within the framework of statistical quantum field theory. We derive the expressions of the spin density matrix and the mean spin vector both for a single quantum relativistic particle and for a quantum free field. After introducing the formalism of the covariant Wigner function for the scalar and the Dirac field, the relation between spin density matrix and the covariant Wigner function is obtained. The formula is applied to the fluid produced in relativistic nuclear collisions by using the local thermodynamic equilibrium density operator and recovering previously known formulae. The dependence of these results on the spin tensor and pseudo-gauge transformations of the stress-energy tensor is addressed., Comment: 24 pages, 1 figure; version published in Lecture Notes in Physics

In view of the recent polarization measurements in ultra-relativistic heavy ion collisions, we discuss the possibility of a physical meaning of the spin angular momentum in quantum field theory and relativistic hydrodynamics., Comment: 4 pages, 1 figure; talk given in the 28th international conference Quark Matter

We calculate the contribution to the polarization of $\Lambda$ hyperons in relativistic nuclear collisions at high energy from the decays of $\Sigma^*(1385)$ and $\Sigma^0$, which are the predominant sources of $\Lambda$ production besides the primary component, as a function of the $\Lambda$ momentum. Particularly, we estimate the longitudinal component of the mean spin vector as a function of the azimuthal angle in the transverse plane, assuming that primary $\Sigma^*$ and $\Sigma^0$ polarization follow the predictions of local thermodynamic equilibrium in a relativistic fluid. Provided that the rapidity dependence around midrapidity of polarization is negligible, we find that this component of the overall spin vector has a very similar pattern to the primary one. Therefore, we conclude that the secondary decays cannot account for the discrepancy in sign between experimental data and hydrodynamic model predictions of the longitudinal polarization of $\Lambda$ hyperons recently measured by the STAR experiment at RHIC., Comment: 16 pages, 2 figures. Final version accepted for publication in EPJ C

We present a general method to determine the entropy current of relativistic matter at local thermodynamic equilibrium in quantum statistical mechanics. Provided that the local equilibrium operator is bounded from below and its lowest lying eigenvector is non-degenerate, it is proved that, in general, the logarithm of the partition function is extensive, meaning that it can be expressed as the integral over a 3D space-like hypersurface of a vector current, and that an entropy current exists. We work out a specific calculation for a non-trivial case of global thermodynamic equilibrium, namely a system with constant comoving acceleration, whose limiting temperature is the Unruh temperature. We show that the integral of the entropy current in the right Rindler wedge is the entanglement entropy., Comment: 12 pages, 1 figure. Published version in Phys Rev D

In this work the non-equilibrium density operator approach introduced by Zubarev more than 50 years ago to describe quantum systems at local thermodynamic equilibrium is revisited. This method - which was used to obtain the first ''Kubo" formula of shear viscosity, is especially suitable to describe quantum effects in fluids. This feature makes it a viable tool to describe the physics of the Quark Gluon Plasma in relativistic nuclear collisions., Comment: 9 pages, 1 figure. Submitted to special issue of Particles: "Nonequilibrium Phenomena in Strongly Correlated System"

The present document discusses plans for a compact, next-generation multi-purpose detector at the LHC as a follow-up to the present ALICE experiment. The aim is to build a nearly massless barrel detector consisting of truly cylindrical layers based on curved wafer-scale ultra-thin silicon sensors with MAPS technology, featuring an unprecedented low material budget of 0.05% X$_0$ per layer, with the innermost layers possibly positioned inside the beam pipe. In addition to superior tracking and vertexing capabilities over a wide momentum range down to a few tens of MeV/$c$, the detector will provide particle identification via time-of-flight determination with about 20~ps resolution. In addition, electron and photon identification will be performed in a separate shower detector. The proposed detector is conceived for studies of pp, pA and AA collisions at luminosities a factor of 20 to 50 times higher than possible with the upgraded ALICE detector, enabling a rich physics program ranging from measurements with electromagnetic probes at ultra-low transverse momenta to precision physics in the charm and beauty sector., Comment: Input to the 2020 Update of the European Particle Physics Strategy

Polarization and chirality are direct manifestations of quantum mechanics in the Quark Gluon Plasma as a relativistic fluid. This is one of the reasons why they are intriguing phenomena, that have attracted so much attention lately. In this talk I will review what is, in my view, the current theoretical understanding and highlight the most interesting recent result., Comment: 7 pages, plenary talk given at the conference Quark Matter 2018. arXiv admin note: text overlap with arXiv:1711.08780

It is shown that the description of a relativistic fluid at local thermodynamic equilibrium depends on the particular quantum stress-energy tensor operator chosen, e.g., the canonical or symmetrized Belinfante stress-energy tensor. We argue that the Belinfante tensor is not appropriate to describe a relativistic fluid whose macroscopic polarization relaxes slowly to thermodynamic equilibrium and that a spin tensor, like the canonical spin tensor, is required. As a consequence, the description of a polarized relativistic fluid involves an extension of relativistic hydrodynamics including a new antisymmetric rank-two tensor as a dynamical field. We show that the canonical and Belinfante tensors lead to different predictions for measurable quantities such as spectrum and polarization of particles produced in relativistic heavy-ion collisions., Comment: 9 pages, 1 figure. Final version to appear in Phys. Lett. B

We calculate the constitutive equations of the stress-energy tensor and the currents of the free massless Dirac field at thermodynamic equilibrium with acceleration and rotation and a conserved axial charge by using the density operator approach. We carry out an expansion in thermal vorticity to the second order with finite axial chemical potential $\mu_A$. The obtained coefficients of the expansion are expressed as correlators of angular momenta and boost operators with the currents. We confirm previous observations that the axial chemical potential induces non-vanishing components of the stress-energy tensor at first order in thermal vorticity due to breaking of parity invariance of the density operator with $\mu_A \ne 0$. The appearance of these components might play an important role in chiral hydrodynamics., Comment: 29 pages, final version published in JHEP, typos

We address the problem of thermodynamic equilibrium with constant acceleration along the velocity field lines in a quantum relativistic statistical mechanics framework. We show that for a free scalar quantum field, after vacuum subtraction, all mean values vanish when the local temperature T is as low as the Unruh temperature T_U = A/2\pi where A is the magnitude of the acceleration four-vector. We argue that the Unruh temperature is an absolute lower bound for the temperature of any accelerated fluid at global thermodynamic equilibrium. We discuss the conditions of this bound to be applicable in a local thermodynamic equilibrium situation., Comment: 15 pages, 2 figures; updated version accepted for publication in Phys. Rev. D

We review the theoretical framework for the calculation of particle polarization in relativistic heavy ion collisions within the hydrodynamical model. The covariant decomposition of the mean spin vector is presented and open theoretical issues addressed., Comment: 6 pages, talk given at Strangeness in Quark Matter conference, Utrecht, July 10-15 2017

We study the polarization of particles in relativistic heavy-ion collisions at very high energy along the beam direction within a relativistic hydrodynamic framework. We show that this component of the polarization decreases much slower with center-of-mass energy compared to the transverse component, even in the ideal longitudinal boost-invariant scenario with non-fluctuating initial state, and that it can be measured by taking advantage of its quadrupole structure in the transverse momentum plane. In the ideal longitudinal boost-invariant scenario, the polarization is proportional to the gradient of temperature at the hadronization and its measurement can provide important information about the cooling rate of the Quark Gluon Plasma around the critical temperature., Comment: 5 pages, 3 figures, final version published in Phys. Rev. Lett

We present a systematic calculation of the corrections of the stress-energy tensor and currents of the free boson and Dirac fields up to second order in thermal vorticity, which is relevant for relativistic hydrodynamics. These corrections are non-dissipative because they survive at general thermodynamic equilibrium with non vanishing mean values of the conserved generators of the Lorentz group, i.e. angular momenta and boosts. Their equilibrium nature makes it possible to express the relevant coefficients by means of correlators of the angular-momentum and boost operators with stress-energy tensor and current, thus making simpler to determine their so-called "Kubo formulae". We show that, at least for free fields, the corrections are of quantum origin and we study several limiting cases and compare our results with previous calculations. We find that the axial current of the free Dirac field receives corrections proportional to the vorticity independently of the anomalous term., Comment: 33 pages, final version published in JHEP, typos

Polarization of $\Lambda$ hyperons and their antiparticles is calculated in a 3+1 dimensional viscous hydrodynamic model with initial state from UrQMD hadron/string cascade. We find that, along with recent results from STAR, the mean polarization at fixed centrality decreases as a function of collision energy from 1.5% at $\sqrt{s_{\rm NN}}=7.7$ GeV to 0.2% at $\sqrt{s_{\rm NN}}=200$ GeV. We explore the effects which lead to such collision energy dependence, feed-down corrections and a difference between $\Lambda$ and $\bar\Lambda$., Comment: contribution to proceedings of Quark Matter 2017, 5-11 February 2017, Chicago (IL)

We calculate the polarization of $\Lambda$ hyperons in Au-Au collisions at RHIC Beam Energy Scan range $\sqrt{s_{\rm NN}}=7.7, \dots, 200$ GeV in a state-of-the-art 3+1 dimensional cascade + viscous hydro model vHLLE+UrQMD. We find that the polarization of $\Lambda$ in the out-of-plane direction decreases substantially with collision energy. We explore the connection between the polarization signal and thermal vorticity and discuss the feed-down and hadronic rescattering effects on the mean polarization of all produced $\Lambda$ hyperons., Comment: proceedings of Strangeness in Quark Matter 2016 conference, 27 June - 1 July 2016, Berkeley

We present a calculation of the global polarization of Lambda hyperons in relativistic Au-Au collisions at RHIC Beam Energy Scan range sqrt{s}_NN = 7.7 - 200 GeV with a 3+1 dimensional cascade + viscous hydro + cascade model, UrQMD+vHLLE. Within this model, the mean polarization of Lambda in the out-of-plane direction is predicted to decrease rapidly with collision energy from a top value of about 2% at the lowest energy examined. We explore the connection between the polarization signal and thermal vorticity and estimate the feed-down contribution to Lambda polarization due to the decay of higher mass hyperons., Comment: 10 pages, 9 figures. Final version published in EPJC

The system created in ultrarelativistic nuclear collisions is known to behave as an almost ideal liquid. In non-central collisions, due to the large orbital momentum, such a system might be the fluid with the highest vorticity ever created under laboratory conditions. Particles emerging from such a highly vorticous fluid are expected to be globally polarized with their spins on average pointing along the system angular momentum. Vorticity-induced polarization is the same for particles and antiparticles, but the intense magnetic field generated in these collisions may lead to the splitting in polarization. In this paper we outline the thermal approach to the calculation of the global polarization phenomenon for particles with spin and we discuss the details of the experimental study of this phenomenon, estimating the effect of feed-down. A general formula is derived for the polarization transfer in two-body decays and, particularly, for strong and electromagnetic decays. We find that accounting for such effects is crucial when extracting vorticity and magnetic field from the experimental data., Comment: 14 pages, 1 figure. Final version published in PRC with one more formula and slightly revised text

The main concepts of general relativistic thermodynamics and general relativistic statistical mechanics are reviewed. The main building block of the proper relativistic extension of the classical thermodynamics laws is the four-temperature vector \beta, which plays a major role in the quantum framework and defines a very convenient hydrodynamic frame. The general relativistic thermodynamic equilibrium condition demands \beta to be a Killing vector field. We show that a remarkable consequence is that all Lie derivatives of all physical observables along the four-temperature flow must then vanish., Comment: 13 pages

We compare the reconstructed hadronization conditions in relativistic nuclear collisions in the nucleon-nucleon centre-of-mass energy range 4.7-2760 GeV in terms of temperature and baryon-chemical potential with lattice QCD calculations, by using hadronic multiplicities. We obtain hadronization temperatures and baryon chemical potentials with a fit to measured multiplicities by correcting for the effect of post-hadronization rescattering. The post-hadronization modification factors are calculated by means of a coupled hydrodynamical-transport model simulation under the same conditions of approximate isothermal and isochemical decoupling as assumed in the statistical hadronization model fits to the data. The fit quality is considerably better than without rescattering corrections, as already found in previous work. The curvature of the obtained "true" hadronization pseudo-critical line kappa is found to be 0.0048 +- 0.0026, in agreement with lattice QCD estimates; the pseudo-critical temperature at vanishing mu_B is found to be 164.3+-1.8 MeV., Comment: 9 pages, 2 figures. Minor corrections, version published in PLB

We study the details and time dependence of particle production in nuclear collisions at a fixed target beam energy of $E_{\mathrm{lab}}= 1.76$ A GeV with the UrQMD transport model. We find that the previously proposed production mechanism for multi strange hadrons, $\phi$ and $\Xi$, are possible due to secondary interactions of incoming nuclei of the projectile and target with already created nuclear resonances, while the Fermi momenta of the nuclei play only a minor role. We also show how the centrality dependence of these particle multiplicities can be used to confirm the proposed mechanism, as it strongly depends on the number of participants in the reaction. Furthermore we investigate the time dependence of particle production in collisions of Ca+Ca at this beam energy, in order to understand the origins of the apparent chemical equilibration of the measured particle yields. We find that indeed the light hadron yields appear to be in equilibrium already from the very early stage of the collision while in fact no local equilibration, through multi collision processes, takes place. The apparent equilibrium is reached only through the decay of the resonances according to available phase space., Comment: 9 pages, 9 figures, version accepted by PRC

We discuss the potential of the experimental programme at NICA to investigate the QCD phase diagram and particularly the position of the critical line at large baryon-chemical potential with accurate measurements of particle multiplicities. We briefly review the present status and we outline the tasks to be accomplished both theoretically and the experimentally to make hadronic abundances a sensitive probe., Comment: 4 pages, 1 figure, to appear in the EPJA Topical Issue on "The NICA White Paper"

This document was prepared by the community that is active in Italy, within INFN (Istituto Nazionale di Fisica Nucleare), in the field of ultra-relativistic heavy-ion collisions. The experimental study of the phase diagram of strongly-interacting matter and of the Quark-Gluon Plasma (QGP) deconfined state will proceed, in the next 10-15 years, along two directions: the high-energy regime at RHIC and at the LHC, and the low-energy regime at FAIR, NICA, SPS and RHIC. The Italian community is strongly involved in the present and future programme of the ALICE experiment, the upgrade of which will open, in the 2020s, a new phase of high-precision characterisation of the QGP properties at the LHC. As a complement of this main activity, there is a growing interest in a possible future experiment at the SPS, which would target the search for the onset of deconfinement using dimuon measurements. On a longer timescale, the community looks with interest at the ongoing studies and discussions on a possible fixed-target programme using the LHC ion beams and on the Future Circular Collider., Comment: 99 pages, 56 figures

We present a new approach to the problem of the thermodynamical equilibrium of a quantum relativistic fluid in a curved spacetime in the limit of small curvature. We calculate the mean value of local operators by expanding the four-temperature Killing vector field in Riemann normal coordinates about the same spacetime point and we derive corrections with respect to the flat spacetime expressions. Thereby, we clarify the origin of the terms proportional to Riemann and Ricci tensors introduced in general hydrodynamic expansion of the stress-energy tensor., Comment: 5 pages

We show that the stress-energy tensor has additional terms with respect to the ideal form in states of global thermodynamic equilibrium in flat spacetime with non-vanishing acceleration and vorticity. These corrections are of quantum origin and their leading terms are second order in the gradients of the thermodynamic fields. Their relevant coefficients can be expressed in terms of correlators of the stress-energy tensor operator and the generators of the Lorentz group. With respect to previous assessments, we find that there are more second order coefficients and that all thermodynamic functions including energy density receive acceleration and vorticity dependent corrections. Notably, also the relation between \rho and p, that is the equation of state, is affected by acceleration and vorticity. We have calculated the corrections for a free real scalar field -- both massive and massless -- and we have found that they increase, particularly for a massive field, at very high acceleration and vorticity and very low temperature. Finally, these non-ideal terms depend on the explicit form of the stress-energy operator, implying that different stress-energy tensor of the scalar field -- canonical or improved -- are thermodynamically inequivalent., Comment: 18 pages, 1 figure. Minor changes, to appear in PRD

We present a quantitative study of vorticity formation in peripheral ultrarelativistic heavy ion collisions at sqrt(s)NN = 200 GeV by using the ECHO-QGP numerical code, implementing relativistic dissipative hydrodynamics in the causal Israel-Stewart framework in 3+1 dimensions with an initial Bjorken flow profile. We consider and discuss different definitions of vorticity which are relevant in relativistic hydrodynamics. After demonstrating the excellent capabilities of our code, which proves to be able to reproduce Gubser flow up to 8 fm/c, we show that, with the initial conditions needed to reproduce the measured directed flow in peripheral collisions corresponding to an average impact parameter b=11.6 fm and with the Bjorken flow profile for a viscous Quark Gluon Plasma with \eta/s=0.1 fixed, a vorticity of the order of some 10^{-2} c/fm can develop at freezeout. The ensuing polarization of Lambda baryons does not exceed 1.4% at midrapidity. We show that the amount of developed directed flow is sensitive to both the initial angular momentum of the plasma and its viscosity., Comment: 13 pages, 22 figures. Minor changes, final version to appear in EPJC

We present an analysis of hadronic multiplicities measured in Pb-Pb collisions at \sqrt s_{NN} = 2.76 TeV as a function of the collision centrality within the statistical hadronization model. Evidence is found of a dependence of the chemical freeze-out temperature as a function of centrality, with a slow rise from central to peripheral collisions, which we interpret as an effect of post-hadronization inelastic scatterings. Using correction factors calculated by means of a simulation based on the UrQMD model, we are able to obtain a significant improvement in the statitical model fit quality and to reconstruct the primordial chemical equilibrium configuration. This is characterized by a nearly constant temperature of about 164 MeV which we interpret as the actual hadronization temperature., Comment: 12 pages, 6 figures. Final version accepted for publication in PRC

We discuss the concept of local thermodynamical equilibrium in relativistic hydrodynamics in flat spacetime in a quantum statistical framework without an underlying kinetic description, suitable for strongly interacting fluids. We show that the appropriate definition of local equilibrium naturally leads to the introduction of a relativistic hydrodynamical frame in which the four-velocity vector is the one of a relativistic thermometer at equilibrium with the fluid, parallel to the inverse temperature four-vector \beta, which then becomes a primary quantity. We show that this frame is the most appropriate for the expansion of stress-energy tensor from local thermodynamical equilibrium and that therein the local laws of thermodynamics take on their simplest form. We discuss the difference between the \beta frame and Landau frame and present an instance where they differ., Comment: 22 pages, 3 figures. To appear in Eur. Phys. J. C

We analyze hadrochemical freeze-out in central Pb+Pb collisions at CERN SPS and LHC energies. Employing the UrQMD hybrid transport model we study the effects of the final hadron/resonance expansion phase on the hadron multiplicities established at hadronization. The bulk meson yields freeze out directly at hadronization whereas the baryon-antibaryon sector is subject to significant alterations, due to annihilation and regeneration processes. We quantify the latter changes by survival factors for each species which are applied to modify the statistical model predictions for the data. The modified SM analysis recovers the hadronization points, which coincide with the recent lattice QCD predictions of the parton-hadron transition line at finite baryochemical potential., Comment: Proceedings of the 8th International Workshop on Critical Point and Onset of Deconfinement, March 11 to 15, 2013 Napa, California, USA

We present ECHO-QGP, a numerical code for $(3+1)$-dimensional relativistic viscous hydrodynamics designed for the modeling of the space-time evolution of the matter created in high energy nuclear collisions. The code has been built on top of the \emph{Eulerian Conservative High-Order} astrophysical code for general relativistic magneto-hydrodynamics [\emph{Del Zanna et al., Astron. Astrophys. 473, 11, 2007}] and here it has been upgraded to handle the physics of the Quark-Gluon Plasma. ECHO-QGP features second-order treatment of causal relativistic viscosity effects in both Minkowskian or Bjorken coordinates; partial or complete chemical equilibrium of hadronic species before kinetic freeze-out; initial conditions based on the optical Glauber model, including a Monte-Carlo routine for event-by-event fluctuating initial conditions; a freeze-out procedure based on the Cooper-Frye prescription. The code is extensively validated against several test problems and results always appear accurate, as guaranteed by the combination of the conservative (shock-capturing) approach and the high-order methods employed. ECHO-QGP can be extended to include evolution of the electromagnetic fields coupled to the plasma., Comment: 25 pages, two column, Final version: accepted for publication in European Physical Journal C

We predict the polarization of Lambda and antiLambda hyperons in peripheral heavy ion collisions at ultrarelativistic energy, based on the assumption of local thermodynamical equilibrium at freeze-out. The polarization vector is proportional to the curl of the inverse temperature four-vector field and its length, of the order of percents, is maximal for particle with moderately high momentum lying on the reaction plane. A selective measurement of these particles could make Lambda polarization detectable., Comment: 5 pages, 3 figures. Revised version

We present an extension of relativistic single-particle distribution function for weakly interacting particles at local thermodynamical equilibrium including spin degrees of freedom, for massive spin 1/2 particles. We infer, on the basis of the global equilibrium case, that at local thermodynamical equilibrium particles acquire a net polarization proportional to the vorticity of the inverse temperature four-vector field. The obtained formula for polarization also implies that a steady gradient of temperature entails a polarization orthogonal to particle momentum. The single-particle distribution function in momentum space extends the so-called Cooper-Frye formula to particles with spin 1/2 and allows to predict their polarization in relativistic heavy ion collisions at the freeze-out., Comment: 15 pages. Final version to appear in Annals of Physics

It is shown that different pairs of stress-energy and spin tensors of quantum relativistic fields related by a pseudo-gauge transformation, i.e. differing by a divergence, imply different mean values of physical quantities in thermodynamical nonequilibrium situations. Most notably, transport coefficients and the total entropy production rate are affected by the choice of the spin tensor of the relativistic quantum field theory under consideration. Therefore, at least in principle, it should be possible to disprove a fundamental stress-energy tensor and/or to show that a fundamental spin tensor exists by means of a dissipative thermodynamical experiment., Comment: 18 pages. Final version accepted for publication in Phys Rev D

We present a Monte-Carlo implementation of the Statistical Hadronization Model in e+e- collisions. The physical scheme is based on the statistical hadronization of massive clusters produced by the event generator Herwig within the microcanonical ensemble. We present a preliminary comparison of several observables with measurements in e+e- collisions at the Z peak. Although a fine tuning of the model parameters is not carried out, a general good agreement between its predictions and data is found., Comment: 19 pages, 28 figures, 6 tables. v2: added sections on comparison between the Statistical Hadronization Model and the Cluster Model and on the interplay between Herwig cluster splitting algorithm and Statistical Hadronization Model predictions. Fixed typos and references added. Version accepted for publication in EPJC

After recapitulating the covariant formalism of equilibrium statistical mechanics in special relativity and extending it to the case of a non-vanishing spin tensor, we show that the relativistic stress-energy tensor at thermodynamical equilibrium can be obtained from a functional derivative of the partition function with respect to the inverse temperature four-vector \beta. For usual thermodynamical equilibrium, the stress-energy tensor turns out to be the derivative of the relativistic thermodynamic potential current with respect to the four-vector \beta, i.e. T^{\mu \nu} = - \partial \Phi^\mu/\partial \beta_\nu. This formula establishes a relation between stress-energy tensor and entropy current at equilibrium possibly extendable to non-equilibrium hydrodynamics., Comment: 4 pages. Final version accepted for publication in Phys. Rev. Lett