TY - CHAP

T1 - Thermodynamic Concepts Out of Equilibrium

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 - Any theoretical approach should not lead to results that contradict the general laws of thermodynamics. However, all concepts of thermodynamics were formed under conditions close to thermodynamic equilibrium. The concept of local thermodynamic equilibrium was introduced for rather slow processes in weakly inhomogeneous systems that made it possible to use all relations of equilibrium thermodynamics locally i.e. in the vicinity of each individual point of the system. For high-speed, high-gradient transport processes accompanied by all the features described in Chapter 2, fundamental difficulties arise with basic thermodynamic concepts which either lose their original meaning or become completely unusable far from local thermodynamic equilibrium. Such concepts require a deep rethinking and revision of their correct using. Moreover, such effects that do not occur near equilibrium require new concepts and approaches for their description. Therefore, in this chapter, we first briefly present the basic concepts and laws of classical thermodynamics, the foundations of linear thermodynamics of irreversible processes that help to solve the problem of closing the transport equations near local equilibrium and then proceed to a critical analysis of the attempts to apply close-to-equilibrium representations to highly non-equilibrium processes. For this analysis we need rigorous results obtained in non-equilibrium statistical thermodynamics described in Chapter 3. Moreover, due to the specific features of processes far from equilibrium, it turned out that in order to describe them, it is necessary to trace the entire thermodynamic evolution of the system under the conditions imposed. The complexity of real processes far from local equilibrium is so great that only synergetic approaches allow us to compress the information and to transfer the description of evolution to the mesoscopic scale level. The order (or control) parameters related to the dynamic mesoscopic structures are not chosen arbitrarily but arise by themselves as a result of self-organization in the system due to nonlinearity, delay and spatial correlations. The system temporal evolution far from local equilibrium should be described on the mesoscale where the internal dynamic structures evolve in a self-consistent way with the macroscopic dynamics of the system. The performed thermodynamic analysis leads us to the conclusion that we need a new interdisciplinary approach to describe such highly non-equilibrium processes as shock-wave processes in condensed media. We hope that the approach presented in Chapter 5 permits to get answers to some important questions of modern thermodynamics.

AB - Any theoretical approach should not lead to results that contradict the general laws of thermodynamics. However, all concepts of thermodynamics were formed under conditions close to thermodynamic equilibrium. The concept of local thermodynamic equilibrium was introduced for rather slow processes in weakly inhomogeneous systems that made it possible to use all relations of equilibrium thermodynamics locally i.e. in the vicinity of each individual point of the system. For high-speed, high-gradient transport processes accompanied by all the features described in Chapter 2, fundamental difficulties arise with basic thermodynamic concepts which either lose their original meaning or become completely unusable far from local thermodynamic equilibrium. Such concepts require a deep rethinking and revision of their correct using. Moreover, such effects that do not occur near equilibrium require new concepts and approaches for their description. Therefore, in this chapter, we first briefly present the basic concepts and laws of classical thermodynamics, the foundations of linear thermodynamics of irreversible processes that help to solve the problem of closing the transport equations near local equilibrium and then proceed to a critical analysis of the attempts to apply close-to-equilibrium representations to highly non-equilibrium processes. For this analysis we need rigorous results obtained in non-equilibrium statistical thermodynamics described in Chapter 3. Moreover, due to the specific features of processes far from equilibrium, it turned out that in order to describe them, it is necessary to trace the entire thermodynamic evolution of the system under the conditions imposed. The complexity of real processes far from local equilibrium is so great that only synergetic approaches allow us to compress the information and to transfer the description of evolution to the mesoscopic scale level. The order (or control) parameters related to the dynamic mesoscopic structures are not chosen arbitrarily but arise by themselves as a result of self-organization in the system due to nonlinearity, delay and spatial correlations. The system temporal evolution far from local equilibrium should be described on the mesoscale where the internal dynamic structures evolve in a self-consistent way with the macroscopic dynamics of the system. The performed thermodynamic analysis leads us to the conclusion that we need a new interdisciplinary approach to describe such highly non-equilibrium processes as shock-wave processes in condensed media. We hope that the approach presented in Chapter 5 permits to get answers to some important questions of modern thermodynamics.

KW - entropy production, information entropy, self-organization, cynergetics, control parameters, mesoscale evolution

UR - https://www.mendeley.com/catalogue/00ea592f-f90d-3eb3-8eae-10f107f59f93/

U2 - 10.1007/978-981-19-2404-0_4

DO - 10.1007/978-981-19-2404-0_4

M3 - Chapter

SN - 978-981-19-2403-3

T3 - Shock Wave and High Pressure Phenomena

SP - 95

EP - 136

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

PB - Springer Nature

CY - Singapore

ER -