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Journal of Physics A Mathematical and General

Thermal processes in the hydrodynamic stage in terms of nonequilibrium thermofield dynamics

Toshihico Arimitsu

Published Dec 21, 1991• 1 citation
Publisher

Abstract

The thermal processes in the hydrodynamic stage are investigated within the formalism of nonequilibrium thermofield dynamics (NETFD) where the concepts in nonequilibrium thermodynamics are implanted. The treatment gives a good indication for an understanding of the new concept, the spontaneous creation of dissipation, in conjunction with the realization of the representation space within NETFD.

DOI
10.1088/0305-4470/24/24/005

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The thermal processes in the hydrodynamic stage are investigated within the formalism of nonequilibrium thermofield dynamics (NETFD) where the concepts in nonequilibrium thermodynamics are implanted. The treatment gives a good indication for an understanding of the new concept, the spontaneous creation of dissipation, in conjunction with the realization of the representation space within NETFD.
A fundamental framework for the construction of a quantum field theory for open systems, which will be called non-equilibrium thermo field dynamics (NETFD), is built upon two concepts. One is the thermal state in the thermal-Liouville space, by which the quasi-particle superoperator is introduced generally from the thermal state condition. The other is the coarse graining which is realized by projecting out some partial space from the complete thermal-Liouville space, and by which the dissipation is introduced. Most properties of the usual quantum field theory (e.g., the operator formalism, the time-ordered formulation of the Green’s functions, the Feynman diagram method in real time, etc.) are preserved in NETFD. The entropy for the nonequilibrium state can be also introduced in NETFD.
The generating functional formulation of non-equilibrium thermo field dynamics (NETFD) is given. The results are compared with those obtained by Schwinger who introduced the forward and backward time axes in order to include the dissipation effect. The relation of NETFD to other closed time-path formalisms is also given. As NETFD is an operator formalism of quantum field theory for non-equilibrium situations, one can say that the usual Green's function formalisms are well founded by NETFD through the comparison given in this paper.
Whether and how a system approaches equilibrium is a central issue in nonequilibrium statistical physics, underpinning our understanding of both thermalization and heat transport. Bogoliubov's three-stage (initial, kinetic, and hydrodynamic) evolution hypothesis provides a qualitative framework, but quantitative advances have mostly been restricted to near-integrable systems such as dilute gases. In this work, we investigate the relaxation dynamics of a one-dimensional diatomic hard-point gas and present a phase diagram that comprehensively characterizes relaxation behavior across the full parameter space, from near-integrable to far-from-integrable regimes. We first analyze thermalization (local energy relaxation in nonequilibrium states) and identify three universal dynamical regimes: (1) In the near-integrable regime, kinetic processes dominate (initial + kinetic phase), local energy relaxation decays exponentially, and the thermalization time τ scales with perturbation strength δ as τ ∝ δ − 2 . (2) In the far-from-integrable regime, hydrodynamic effects dominate (initial + hydrodynamic phase), local energy relaxation follows power-law decay, and thermalization time scales linearly with system size N . (3) In the intermediate regime, Bogoliubov phase emerges, marked by the transition from kinetic to hydrodynamic relaxation. The phase diagram further reveals that hydrodynamic behavior can emerge even in small systems when the system is sufficiently far from the integrable regime, challenging the conventional view that such effects are only significant in large systems. In the thermodynamic limit, the system's relaxation behavior depends on the order in which the limits ( N → ∞ or δ → 0 ) are taken. We then turn to heat transport (decay of heat-current fluctuations in equilibrium) and demonstrate that its behavior is fully consistent with the thermalization process, leading to the first unified theoretical description of thermalization and heat transport. Our results establish a comprehensive view of relaxation in classical many-body systems and suggest a route for studying similar dynamics in quantum systems, highlighting universal scaling laws and the interplay of kinetic and hydrodynamic processes across integrability regimes.
Bringing together the key ideas from nonequilibrium statistical mechanics and powerful methodology from quantum field theory, this book captures the essence of nonequilibrium quantum field theory. Beginning with the foundational aspects of the theory, the book presents important concepts and useful techniques, discusses issues of basic interest, and shows how thermal field, linear response, kinetic theories and hydrodynamics emerge. It also illustrates how these concepts and methodology are applied to current research topics including nonequilibrium phase transitions, thermalization in relativistic heavy ion collisions, the nonequilibrium dynamics of Bose-Einstein condensation, and the generation of structures from quantum fluctuations in the early Universe. Divided into five parts, with each part addressing a particular stage in the conceptual and technical development of the subject, this self-contained book is a valuable reference for graduate students and researchers in particle physics, gravitation, cosmology, atomic-optical and condensed matter physics.