Related papers: Thermodynamics of chaotic relaxation processes
We study the energy flow between a one dimensional oscillator and a chaotic system with two degrees of freedom in the weak coupling limit. The oscillator's observables are averaged over an initially microcanonical ensemble of trajectories…
The thermodynamic formalism, which was first developed for dynamical systems and then applied to discrete Markov processes, turns out to be well suited for continuous time Markov processes as well, provided the definitions are interpreted…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
We reveal a correspondence between temperature and integrability-breaking in classical and quantum many-body systems through the lens of geometry and adiabatic transformations. Decreasing the temperature, obtained in a standard way through…
In systems with detailed balance, the stationary distribution and the equilibrium distribution are identical, creating a clear connection between energetic and entropic quantities. Many driven systems violate detailed balance and still pose…
Thermodynamical arguments are known to be useful in the construction of physically motivated Lyapunov functionals for nonlinear stability analysis of spatially homogeneous equilibrium steady states in thermodynamically isolated systems.…
The Heat theorem reveals the second law of equilibrium Thermodynamics (i.e.existence of Entropy) as a manifestation of a general property of Hamiltonian Mechanics and of the Ergodic Hypothesis, valid for 1 as well as $10^{23}$ degrees of…
Uniformity of the probability measure of phase space is considered in the framework of classical equilibrium thermodynamics. For the canonical and the grand canonical ensembles, relations are given between the phase space uniformities and…
The dynamics of the kicked-rotor, that is a paradigm for a mixed system, where the motion in some parts of phase space is chaotic and in other parts is regular is studied statistically. The evolution (Frobenius-Perron) operator of phase…
The heat theorem (i.e. the second law of thermodynamics or the existence of entropy) is a manifestation of a general property of hamiltonian mechanics and of the ergodic Hypothesis. In nonequilibrium thermodynamics of stationary states the…
We study phase transitions in the thermodynamic description of Pomeau-Manneville intermittent maps from the point of view of infinite ergodic theory, which deals with diverging measure dynamical systems. For such systems, we use a…
We study a dynamical system with time dependent Hamiltonian by numerical experiments so as to find a relation between thermodynamics and chaotic nature of the system. Excess information loss, defined newly based on Lyapunov analysis, is…
Equilibrium properties of many-body systems with a large number of degrees of freedom are generally expected to be described by statistical mechanics. Such expectations are closely tied to the observation of thermalization, as manifested…
We study an ensemble of identical noisy phase oscillators with a blinking mean-field coupling, where one-cluster and two-cluster synchronous states alternate. In the thermodynamic limit the population is described by a nonlinear…
Linking thermodynamic variables like temperature $T$ and the measure of chaos, the Lyapunov exponents $\lambda$, is a question of fundamental importance in many-body systems. By using nonlinear fluid equations in one and three dimensions,…
Various kinematical quantities associated with the statistical properties of dynamical systems are examined: statistics of the motion, dynamical bases and Lyapunov exponents. Markov partitons for chaotic systems, without any attempt at…
Phase space representations of the dynamics of the quantal and classical cat map are used to explore quantum--classical correspondence in a K-system: as $\hbar \to 0$, the classical chaotic behavior is shown to emerge smoothly and exactly.…
We study the dynamics of non interacting thermal atoms embedded in structured optical lattices with non trivial geometry. The lattice would be generated by two counter propagating modes with parabolic cylindrical symmetry and we concentrate…
The article presents results of preliminary study of solutions to recently offered basic thermodynamic equation for equilibrium in chemical systems with focus on chaotic behavior. Classical part of that equation was investigated earlier in…
We develop a theory describing the transition to a spatially homogeneous regime in a mixing flow with a chaotic in time reaction. The transverse Lyapunov exponent governing the stability of the homogeneous state can be represented as a…