TY - CHAP

T1 - Macroscopic Description in Terms of Non-Equilibrium Statistical Mechanics.

AU - Хантулева, Татьяна Александровна

N1 - Bibliographic Information • Book Title Mathematical Modeling of Shock-Wave Processes in Condensed Matter • Book Subtitle From Statistical Thermodynamics to Control Theory • Authors Tatiana Aleksandrovna Khantuleva • Series Title Shock Wave and High Pressure Phenomena • DOI https://doi.org/10.1007/978-981-19-2404-0 • Publisher Springer Singapore • eBook Packages Physics and Astronomy, Physics and Astronomy (R0) • Copyright Information The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 • Hardcover ISBN 978-981-19-2403-3 • eBook ISBN 978-981-19-2404-0 • Series ISSN 2197-9529 • Series E-ISSN 2197-9537 • Edition Number1 • Number of Pages XV, 336 • Number of Illustrations 19 b/w illustrations, 58 illustrations in colour • Topics Statistical Physics, Classical and Continuum Physics, Condensed Matter, Solid Mechanics

PY - 2022/7/19

Y1 - 2022/7/19

N2 - A critical analysis of the current situation with the description of non-equilibrium transport processes allows us to conclude that in order to describe non-equilibrium processes it is necessary to go to a deeper level of description in comparison with the average, macroscopic one. Such a description based on the so called “first principles” is provided by non-equilibrium statistical mechanics. The goal of statistical mechanics is to create a consistent and efficient formalism for describing the macroscopic behavior of many-particle systems based on microscopic theory. Non-equilibrium statistical mechanics provides approaches and tools for describing irreversible processes in real systems within the framework of a unified theoretical method allowing one to calculate, albeit approximately, the transport coefficients that characterize the system relaxation to equilibrium. The most constructive result in non-equilibrium statistical mechanics is the proof of the fact that the equations describing the behavior of a non-equilibrium thermodynamic system in terms of an incomplete set of variables can no longer be purely differential that is, local in space and time. A fruitful statistical-mechanical method for describing non-equilibrium processes of mass, momentum and energy transport was proposed by D.N. Zubarev [1-3]. Here we briefly consider the method and the main results obtained in its framework. The space-time integral relationships between the conjugate fluxes and macroscopic gradients of momentum and energy densities obtained on the basis of the non-equilibrium statistical operator method contain relaxation transport kernels which generalize the transport coefficients to non-equilibrium conditions.Integro-differential equations of nonlocal hydrodynamics generalize the equations of classical hydrodynamics to non-equilibrium processes beyond the validity of continuum mechanics. A characteristic feature of the new description is the preservation of integral information about the system in the generalized hydrodynamic equations when describing its local properties. The effects of the spatiotemporal nonlocality are the price that one has to pay for the inevitable incompleteness of the macroscopic description of non-equilibrium processes in open systems. The nonlocal transport equations with memory will serve as the basis for the new approach proposed in Chapter 5 of this book which will be able to describe highly non-equilibrium processes.

AB - A critical analysis of the current situation with the description of non-equilibrium transport processes allows us to conclude that in order to describe non-equilibrium processes it is necessary to go to a deeper level of description in comparison with the average, macroscopic one. Such a description based on the so called “first principles” is provided by non-equilibrium statistical mechanics. The goal of statistical mechanics is to create a consistent and efficient formalism for describing the macroscopic behavior of many-particle systems based on microscopic theory. Non-equilibrium statistical mechanics provides approaches and tools for describing irreversible processes in real systems within the framework of a unified theoretical method allowing one to calculate, albeit approximately, the transport coefficients that characterize the system relaxation to equilibrium. The most constructive result in non-equilibrium statistical mechanics is the proof of the fact that the equations describing the behavior of a non-equilibrium thermodynamic system in terms of an incomplete set of variables can no longer be purely differential that is, local in space and time. A fruitful statistical-mechanical method for describing non-equilibrium processes of mass, momentum and energy transport was proposed by D.N. Zubarev [1-3]. Here we briefly consider the method and the main results obtained in its framework. The space-time integral relationships between the conjugate fluxes and macroscopic gradients of momentum and energy densities obtained on the basis of the non-equilibrium statistical operator method contain relaxation transport kernels which generalize the transport coefficients to non-equilibrium conditions.Integro-differential equations of nonlocal hydrodynamics generalize the equations of classical hydrodynamics to non-equilibrium processes beyond the validity of continuum mechanics. A characteristic feature of the new description is the preservation of integral information about the system in the generalized hydrodynamic equations when describing its local properties. The effects of the spatiotemporal nonlocality are the price that one has to pay for the inevitable incompleteness of the macroscopic description of non-equilibrium processes in open systems. The nonlocal transport equations with memory will serve as the basis for the new approach proposed in Chapter 5 of this book which will be able to describe highly non-equilibrium processes.

KW - statistical mechanics, non-equilibrium distribution function, spatiotemporal correlations, nonlocal and memory effects, nonlocal hydrodynamics

UR - https://www.mendeley.com/catalogue/1347a399-c0ba-3cf5-bcaa-7902b2790b18/

U2 - 10.1007/978-981-19-2404-0_3

DO - 10.1007/978-981-19-2404-0_3

M3 - Chapter

SN - 978-981-19-2403-3

T3 - Shock Wave and High Pressure Phenomena

SP - 65

EP - 94

BT - Mathematical Modeling of Shock-Wave Processes in Condensed Matter

PB - Springer Nature

CY - Singapore

ER -