Entropy and uncertainty of squeezed quantum open systems

Abstract

We define the entropy S and uncertainty function of a squeezed system interacting with a thermal bath, and study how they change in time by following the evolution of the reduced density matrix in the influence functional formalism. As examples, we calculate the entropy of two exactly solvable squeezed systems: an inverted harmonic oscillator and a scalar field mode evolving in an inflationary universe. For the inverted oscillator with weak coupling to the bath, at both high and low temperatures, S → r, where r is the squeeze parameter. In the de Sitter case, at high temperatures, S → (1 − c)r where c = γ 0 /H, γ 0 being the coupling to the bath and H the Hubble constant. These three cases confirm previous results based on more ad hoc prescriptions for calculating entropy. But at low temperatures, the de Sitter entropy S → (1/2 − c)r is noticeably different. This result, obtained from a more rigorous approach, shows that factors usually ignored by the conventional approaches, i.e., the nature of the environment and the coupling strength betwen the system and the environment, are important.

Entropy of gravitons produced in the early universe

“…For complete randomization, one would thus have to invoke, for example, a thermal bath at a sufficiently high temperature. Such a model was discussed in [15], and their results seem to be consistent with our general treatment. Conditions similar to (9) and (12) have been frequently discussed in quantum mechanics, see e.g.…”

Correlation entropy of an interacting quantum field andHtheorem for theO(N)model

“…(So far it has only been implemented within the framework of perturbation theory.) Another equally powerful method adept to field theory is the Feynman-Vernon influence functional formalism [27,15] which has been used to treat entropy in quantum open systems (see, e.g., [28]). …”

“…Various proposals for coarse graining the dynamics of parametric oscillators have followed [31,32,33,34,35]. The language of squeezed states is particularly useful for describing entropy growth due to parametric particle creation [36,37,33,28]. For our purposes, the essential features of entropy growth due to parametric particle creation which distinguish it from correlational entropy growth (to be discussed below), are that parametric particle creation depends sensitively on the choice of representation for the state space of the parametric oscillators, and the specificity of the initial conditions.…”

Finding the probability distribution of states in the fuzzy markov systems

“…The nonexponentiality of the processes of systems being in their possible states they predetermines the expediency of applying in the problems of analysis and synthesis of real systems a more flexible mathematical apparatus -the theory of semi-Markov processes (SMP). Technologies of solving such problems under conditions of SMP are well developed and efficient [13][14][15].…”