We consider causal higher order theories of relativistic viscous hydrodynamics in the limit of onedimensional boost-invariant expansion and study the associated dynamical attractor. We obtain evolution equations for the inverse Reynolds number as a function of Knudsen number. The solutions of these equations exhibit attractor behavior which we analyze in terms of Lyapunov exponents using several different techniques. We compare the attractors of the second-order Müller-Israel-Stewart (MIS), transient Denicol-Niemi-Molnar-Rischke (DNMR), and third-order theories with the exact solution of the Boltzmann equation in the relaxation-time approximation. It is shown that for Bjorken flow the third-order theory provides a better approximation to the exact kinetic theory attractor than both MIS and DNMR theories. For three different choices of the time dependence of the shear relaxation rate we find analytical solutions for the energy density and shear stress and use these to study the attractors analytically. By studying these analytical solutions at both small and large Knudsen numbers we characterize and uniquely determine the attractors and Lyapunov exponents. While for small Knudsen numbers the approach to the attractor is exponential, strong power-law decay of deviations from the attractor and rapid loss of initial state memory is found even for large Knudsen numbers. Implications for the applicability of hydrodynamics in far-offequilibrium situations are discussed.

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In this article, there are 18 sections discussing various current topics in the field of relativistic heavy-ion collisions and related phenomena, which will serve as a snapshot of the current state of the art. Section 1 reviews experimental results of some recent light-flavored particle production data from ALICE collaboration. Other sections are mostly theoretical in nature. Very strong but transient magnetic field created in relativistic heavy-ion collisions could have important observational consequences. This has generated a lot of theoretical activity in the last decade. Sections 2, 7, 9, 10 and 11 deal with the effects of the magnetic field on the properties of the QCD matter. More specifically, Sec. 2 discusses mass of [Formula: see text] in the linear sigma model coupled to quarks at zero temperature. In Sec. 7, one-loop calculation of the anisotropic pressure are discussed in the presence of strong magnetic field. In Sec. 9, chiral transition and chiral susceptibility in the NJL model is discussed for a chirally imbalanced plasma in the presence of magnetic field using a Wigner function approach. Sections 10 discusses electrical conductivity and Hall conductivity of hot and dense hadron gas within Boltzmann approach and Sec. 11 deals with electrical resistivity of quark matter in presence of magnetic field. There are several unanswered questions about the QCD phase diagram. Sections 3, 11 and 18 discuss various aspects of the QCD phase diagram and phase transitions. Recent years have witnessed interesting developments in foundational aspects of hydrodynamics and their application to heavy-ion collisions. Sections 12 and 15–17 of this article probe some aspects of this exciting field. In Sec. 12, analytical solutions of viscous Landau hydrodynamics in 1+1D are discussed. Section 15 deals with derivation of hydrodynamics from effective covariant kinetic theory. Sections 16 and 17 discuss hydrodynamics with spin and analytical hydrodynamic attractors, respectively. Transport coefficients together with their temperature- and density-dependence are essential inputs in hydrodynamical calculations. Sections 5, 8 and 14 deal with calculation/estimation of various transport coefficients (shear and bulk viscosity, thermal conductivity, relaxation times, etc.) of quark matter and hadronic matter. Sections 4, 6 and 13 deal with interesting new developments in the field. Section 4 discusses color dipole gluon distribution function at small transverse momentum in the form of a series of Bells polynomials. Section 6 discusses the properties of Higgs boson in the quark–gluon plasma using Higgs–quark interaction and calculate the Higgs decays into quark and anti-quark, which shows a dominant on-shell contribution in the bottom-quark channel. Section 13 discusses modification of coalescence model to incorporate viscous corrections and application of this model to study hadron production from a dissipative quark–gluon plasma.

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