This paper considers solving optimization problem for linear discrete time systems such that closed-loop discrete-time system is positive (i.e., all of its state variables have non-negative values) and also finite-time stable. For this purpose, by considering a quadratic cost function, an optimal controller is designed such that in addition to minimizing the cost function, the positivity proper...

We study the finite size scaling of the spin stiffness for the one-dimensional s = 1 2 quantum antiferromagnet as a function of the anisotropy parameter ∆. Previous Bethe ansatz results allow a determination of the stiffness in the thermodynamic limit. The Bethe ansatz equations for finite systems are solvable even in the presence of twisted boundary conditions, a fact we exploit to determine t...

The present review is devoted to the problems of finite-size scaling due to the presence of long-range interaction decaying at large distance as 1/rd+σ, where d is the spatial dimension and the long-range parameter σ > 0. Classical and quantum systems are considered. 1. Finite-size systems and critical phenomena A common wisdom is that the singularities in the thermodynamic functions at a criti...

The study of time has a long history and is still ongoing. term formulated by Isaac Newton was coined in the 17th century, so naturally it could not relate to thermodynamics. Since passage aging are inalienable components human experience, Newton's concept alive. W.G. Leibniz I. Kant mainly questioned absoluteness time. This paper introduces definition justifies thesis that thermodynamic proces...

We discuss the role of Bose enhancement of the dipole matrix element in photoassociation, using stimulated Raman adiabatic passage as an example. In a nondegenerate gas the time scale for coherent optical transients tends to infinity in the thermodynamic limit, whereas Bose enhancement keeps this time scale finite in a condensate. Coherent transients are therefore absent in photoassociation of ...

An apparent paradox in classical statistical physics is the mechanism by which conservative. time-reversible microscopic dynamics, can pive rise to seemi,ngly dissipative behavior. In this paper we use system theoretic mols to show that dissipation can arise as an anifact of incomplete observations over a finite horizon. In addition, this approach allows us to obtain finile-time. low order, app...

“Staging free energy” is a term introduced to describe the necessary investment of free energy into a thermodynamic system to allow certain near equilibrium processes to proceed in a desired direction and in finite time (Chapter 4). Such processes may seem—if viewed detached from their surroundings—to be truly reversible. However, if one views them together with the changes occurring in their e...