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Considering the interaction among matter, vacuum, and radiation, this paper investigates the evolution of cosmic dynamics of the varying-vacuum model in a case of Finslerian geometry through dynamic analysis methods. Surprisingly, this model can alleviate the coincidence problem and allows for a stable later cosmological solution corresponding to the accelerating universe. [ABSTRACT FROM AUTHOR]

Any given density matrix can be represented as an infinite number of ensembles of pure states. This leads to the natural question of how to uniquely select one out of the many, apparently equally-suitable, possibilities. Following Jaynes' information-theoretic perspective, this can be framed as an inference problem. We propose the Maximum Geometric Quantum Entropy Principle to exploit the notions of Quantum Information Dimension and Geometric Quantum Entropy. These allow us to quantify the entropy of fully arbitrary ensembles and select the one that maximizes it. After formulating the principle mathematically, we give the analytical solution to the maximization problem in a number of cases and discuss the physical mechanism behind the emergence of such maximum entropy ensembles. [ABSTRACT FROM AUTHOR]