Abstract
We present a new derivation of second-order relativistic dissipative fluid dynamics for quantum systems using Zubarev’s formalism for the non-equilibrium statistical operator. In particular, we discuss the shear-stress tensor to second order in gradients and argue that the relaxation terms for the dissipative quantities arise from memory effects contained in the statistical operator. We also identify new transport coefficients which describe the relaxation of dissipative processes to second order and express them in terms of equilibrium correlation functions, thus establishing Kubo-type formulae for the second-order transport coefficients.
Highlights
Fluid dynamics is a powerful tool to describe low-frequency and long-wavelength phenomena in statistical systems [1]
We present a new derivation of second-order relativistic dissipative fluid dynamics for quantum systems using Zubarev’s formalism for the non-equilibrium statistical operator
We identify new transport coefficients which describe the relaxation of dissipative processes to second order and express them in terms of equilibrium correlation functions, establishing Kubo-type formulae for the second-order transport coefficients
Summary
Fluid dynamics is a powerful tool to describe low-frequency and long-wavelength phenomena in statistical systems [1]. We adopt the method of the non-equilibrium statistical operator (NESO) [6,7] to obtain the relativistic fluid-dynamical equations of motion for strongly correlated matter, such as the QGP, in the non-perturbative regime. The method was applied to quantum fields [8] and has been since extended to treat systems in strong magnetic fields [9] It is based on a generalization of the Gibbs canonical ensemble to non-equilibrium states, i.e., the statistical operator is promoted to a non-local functional of the thermodynamic parameters and their space-time derivatives. There exist a number of formulations of relativistic fluid dynamics in terms of near-equilibrium quantities which are related to the NESO method employed by us; for recent work, see References [10,11,12].
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