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Using flow equations, equilibrium and non-equilibrium dynamics of a two-level system are investigated, which couples via non-commuting components to two independent oscillator baths. In equilibrium the two-level energy splitting is…
We investigate a two-level system in resonant contact with a larger environment. The environment typically is in a canonical state with a given temperature initially. Depending on the precise spectral structure of the environment and the…
We consider initial-boundary problems for general linear first-order strictly hyperbolic systems with local or nonlocal nonlinear boundary conditions. While boundary data are supposed to be smooth, initial conditions can contain…
We simulate the evolution of one-dimensional gravitating collisionless systems from non- equilibrium initial conditions, similar to the conditions that lead to the formation of dark- matter halos in three dimensions. As in the case of 3D…
One of the major problems in the theory of the porous medium equation is the regularity of the solutions and the free boundaries. Here we assume flatness of the solution in space time cylinder and derive smoothness of the interface after a…
This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…
A framework for the non-equilibrium thermodynamics of glasses is discussed. It also explains the non-equilibrium thermodynamics of a black hole isolated from matter. The first and second laws of black dynamics and black hole thermodynamics…
We reveal the emergence of environment-induced spontaneous synchronization between two spin-1/2 quantum objects in a collision model setting. In particular, we determine the conditions for the dynamical establishment of synchronous…
We describe a one-dimensional self-gravitating system derived from the problem of large-scale structure formation in cosmology. Considering small times so that the expansion can be neglected we present a thermodynamical analysis of this…
The free cooling process in the inelastic hard sphere system is studied by analysing the data from large scale molecular dynamics simulations on a three dimensional system. The initial energy decay, the velocity distribution function, and…
This paper studies Mullins' model of thermal grooving which consists of a surface diffusion flow equation with contact angle and no-flux boundary conditions. We consider this problem in a multi-dimensional half space and prove that if the…
Simulations of purely self-gravitating N-body systems are often used in astrophysics and cosmology to study the collisionless limit of such systems. Their results for macroscopic quantities should then converge well for sufficiently large…
Results of numerical simulation constructed before strict mathematical model of an establishment of thermodynamic equilibrium in originally nonequilibrium cosmological ultrarelativistic plasma for the Universe with any acceleration in the…
In self-gravitating stars, two dimensional or geophysical flows and in plasmas, long range interactions imply a lack of additivity for the energy; as a consequence, the usual thermodynamic limit is not appropriate. However, by contrast with…
Entanglement asymmetry has emerged as a powerful tool for characterizing symmetry breaking in quantum many-body systems. In this Letter, we explore how symmetry is dynamically broken through the lens of entanglement asymmetry in two…
A model glass with fast and slow processes is studied. The statics is simple and the facilitated slow dynamics is exactly solvable. The main features of a fragile glass take place: Kauzmann transition, Vogel-Fulcher law, Adam-Gibbs relation…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
We study the initial value problem of the thermal-diffusive combustion system: $u_{1,t} = u_{1,x,x} - u_1 u^2_2, u_{2,t} = d u_{2,xx} + u_1 u^2_2, x \in R^1$, for non-negative spatially decaying initial data of arbitrary size and for any…
We study the issue of temperature in a steady system around a black hole event horizon, contrasting it with the appearance of divergence in a thermal equilibrium system. We focus on a spherically symmetric system governed by general…
We consider solutions to linear parabolic equations with initial data decaying at spatial infinity. For a class of advection-diffusion equations with a spatially dependent velocity field, we study the behavior of solutions as time tends to…