Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
41 (2000), S. 7445-7457
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
In this paper we investigate the kinetic foundation of extended irreversible thermodynamics via the moment method. First we consider the construct of the 1-particle distribution function f in terms of its moments by maximizing the entropy density function. We then project f from its L2 space onto the local thermodynamic variables z=(z1,...,zN) in the thermodynamic base space B(circumflex)N. Thus instead of the Boltzmann equation we consider a set of evolution equations of z in B(circumflex)N. Second, we formulate the laws of thermodynamics governing the variable z in B(circumflex)N. These laws exhibit an intrinsic geometric structure of thermodynamics in the setting of contact geometry. Finally, as an illustration, we discuss the evolution equations for the bulk pressure Pb, heat flux Q, and the symmetric traceless tensor π(two down arrows) corresponding to the viscous and heat conduction irreversible processes. These equations can be formulated as an abstract inhomogeneous hyperbolic evolution equation. By employing the C0 semigroup technique, we discuss the solution of the evolution equation and its asymptotic behavior. We show that thermodynamic stability condition of the system implies asymptotic dynamical stability of the solution and vice versa. © 2000 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.1312194
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