TL;DR: For a subshift X, h(/z) will stand for the entropy of a tz E rig(X), and C(X) is the set of continuous real-valued functions on X, and d//( X) theset of shiftinvariant Borel probability measures on X is defined.
Abstract: More generally, we consider the subshifts of F z. These are the closed subsets of F z that are invariant under S. We denote for such a subshift X by C(X) the set of continuous real-valued functions on X, and by d//(X) the set of shiftinvariant Borel probability measures on X. h(/z) will stand for the entropy of a tz E rig(X). (For the entropy and its properties see, e.g., [11].) We set for a subshift X,
TL;DR: In this article, the authors studied the relaxation dynamics of a microcanonical two-dimensional self-gravitating system and quantitatively described the final stationary state, without any adjustable parameters.
Abstract: We study, using both theory and molecular dynamics simulations, the relaxation dynamics of a microcanonical two dimensional self-gravitating system. After a sufficiently large time, a gravitational cluster of N particles relaxes to the Maxwell-Boltzmann distribution. The time to reach the thermodynamic equilibrium, however, scales with the number of particles. In the thermodynamic limit, $N\to\infty$ at fixed total mass, equilibrium state is never reached and the system becomes trapped in a non-ergodic stationary state. An analytical theory is presented which allows us to quantitatively described this final stationary state, without any adjustable parameters.
TL;DR: In this paper, a general thermodynamic strain space formulation of rate independent plasticity by means of plastic internal variables is presented, with the plastic work being the only plastic internal variable and necessary and sufficient consitbns on the elastic moduli and their change with plastic deformation are derived.
TL;DR: In this article, a new postulate of extended irreversible thermodynamics is suggested, which, in case of a stationary states, reduces to the local equilibrium hypothesis on the basis of this postulate, a transport equation of the dual phase-lag model of heat transfer is derived.