Related papers: Entropy decay for the Kac evolution
An analytical solution to the time evolution of decay of one and two identical noninteracting particles is presented using the formalism of resonant states. It is shown that the time-dependent wave function and hence the survival and…
The initial boundary value problem for a system of viscoelastic wave equations of Kirchhoff type with strong damping is considered. We prove that, under suitable assumptions on relaxation functions and certain initial data, the decay rate…
A condition which guaranties the exponential decay of the solutions of the initial-boundary value problem for the damped wave equation is proved. A method for the effective computability of the coefficient of exponential decay is also…
A statistical-mechanical investigation is performed on Rayleigh-B\'enard convection of a dilute classical gas starting from the Boltzmann equation. We first present a microscopic derivation of basic hydrodynamic equations and an expression…
We consider Pimsner algebras that arise from C*-correspondences of finite rank, as dynamical systems with their rotational action. We revisit the Laca-Neshveyev classification of their equilibrium states at positive inverse temperature…
Within an inherently classical perspective, there is always an unavoidable energy cost associated with the information deletion and this common lore is at the heart of the Landauer's conjecture that does not impose, per se, any relevant…
We consider the linear growth-fragmentation equation arising in the modelling of cell division or polymerisation processes. For constant coefficients, we prove that the dynamics converges to the steady state with an exponential rate. The…
Considering a kicked rotor coupled to a model heat bath both the classical and quantum entropy productions are calculated exactly. Starting with an initial wave packet, the von Neuman entropy as a function of time is determined from the…
A quantum coordinate-entropy formulated in quantum phase space has been recently proposed together with an entropy law that asserts that such entropy can not decrease over time. The coordinate-entropy is dimensionless, a relativistic…
Using the stochastic thermodynamics, we determine the entropy production and the dynamic heat capacity of systems subject to a sinusoidally time dependent temperature, in which case the systems are permanently out of thermodynamic…
The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which detailed balance and time-reversal symmetry are broken. Despite…
Energy decay is established for the damped wave equation on compact Riemannian manifolds where the damping coefficient is allowed to depend on time. Using a time dependent observability inequality, it is shown that the energy of solutions…
We obtain estimates on the exponential rate of decay of the relative entropy from equilibrium for Markov processes with a non-local infinitesimal generator. We adapt some of the ideas coming from the Bakry-Emery approach to this setting. In…
We prove existence of the largest and the smallest entropy solutions to the Cauchy problem for a nonlinear degenerate anisotropic parabolic equation. Applying this result, we establish the comparison principle in the case when at least one…
We study the entropy production in a macroscopic nonequilibrium system that undergoes an order-disorder phase transition. Entropy production is a characteristic feature of nonequilibrium dynamics with broken detailed balance. It is found…
We consider thermodynamic systems with finitely many degrees of freedom and subject to an external control action. We derive some basic results on the dependence of the relative entropy production rate on the controlling force. Applications…
Entropy generation in a chemical reaction is analyzed without using the general formalism of non-equilibrium thermodynamics at a level adequate for advanced undergraduates. In a first approach to the problem, the phenomenological kinetic…
The concept of entropy in nonequilibrium macroscopic systems is investigated in the light of an extended equation of motion for the density matrix obtained in a previous study. It is found that a time-dependent information entropy can be…
We study the non-autonomous version of an infinite-dimensional port-Hamiltonian system on an interval $[a, b]$. Employing abstract results on evolution families, we show $C^1$-well-posedness of the corresponding Cauchy problem, and thereby…
In a glassy system different degrees of freedom have well-separated characteristic times, and are described by different temperatures. The stationary state is essentially non-equilibrium. A generalized statistical thermodynamics is…