Thermodynamics is a core part of most science and engineering curricula. However, most texts that are currently available to students still treat thermodynamics very much as it was presented in the 19th century,...

This work is focused on the dissipative system

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...

Let L be a second order elliptic operator on R with a constant diffusion matrix and a dissipative (in a weak sense) drift b ∈ L loc with some p > d. We assume that L possesses a Lyapunov function, but no local boundedness of b is assumed. It is known that then there exists a unique probability measure μ satisfying the equation Lμ = 0 and that the closure of L in L1(μ) generates a Markov semigro...

Using the methods of quantum trajectories we study effects of dissipative decoherence on the accuracy of the Grover quantum search algorithm. The dependence on the number of qubits and dissipation rate are determined and tested numerically with up to 16 qubits. As a result, our numerical and analytical studies give the universal law for decay of fidelity and probability of searched state which ...

This paper provides a Lyapunov-based small-gain theorem for input-to-state stability (ISS) of networks composed infinitely many finite-dimensional systems. We model these on infinite-dimensional ? ? -type spaces. A crucial assumption in our results is that the internal Lyapunov gains, modeling influence subsystems each other, are linear functions. Moreover, gain operator built from gains assume...

Let A be the generator of a (C„) contraction semigroup on a Banach space. Let B be a dissipative operator with densely defined adjoint. Assume that the inequality H&cj|^|M:r|| + holds on the domain of A. Then the closure of /f + B generates a (C0) contraction semigroup. Let A be the generator of a (C0) contraction semigroup on a Banach space X. Let B be a dissipative operator on X in the sense ...

We present a method for model reduction based on ideas from the behavioral theory of dissipative systems, in which the reduced-order model is required to reproduce a subset of the set of trajectories of minimal dissipation of the original system. The passivity-preserving model reduction method of Antoulas and Sorensen proposed in [2, 19] is shown to be a particular case of this more general cla...