Our results show that an ensemble of S-systems could be interpreted as a collection of structurally indistinguishable and unidentifiable models [ 19].
Within statistical energy analysis (SEA), the coupling loss factor (CLF) is a statistical quantity defined in terms of the average behaviour of an ensemble of similar systems.
In contrast to conventional approaches based on average Hamiltonian theory, the concept of optimal tracking is used: a pulse sequence is designed that steers the evolution of an ensemble of spin systems such that at a series of time points, a specified trajectory of the density operator is tracked as closely as possible.
Hence, if one demands that an ensemble of isolated systems describing thermal equilibrium must be represented by a stationary distribution, the only choice for this purpose is the micro-canonical one.
An ensemble of plate systems is defined, and analytical expressions are found for the ensemble average input and coupling powers which result from "rain-on-the-roof" excitation of one of the plates.
Concepts of the older theory (volume, pressure, temperature, entropy) must be related to the concepts of the newer theory (molecular constitution, dynamical concepts governing the motion of the molecular constituents, probabilistic notions characterizing either the states of an individual system or distributions of states over an imagined ensemble of systems subject to some common constraints).
Another motivation is to make comparison between external noise-induced behaviors in the single toggle switch system and in an ensemble of toggle switch systems aforementioned.
Through local linearizations of the nonlinear drift fields in the process/observation equations via explicit Ito Taylor expansions, the given nonlinear system is transformed into an ensemble of locally linearized systems.
In particular, if we have a huge ensemble of systems each prepared in the same quantum state, the more the position is narrowed down, the less the velocity is, and vice versa.
We were able to obtain a complete ensemble of systems dissolving within ∼180 crossing times.
