Entropy and induced dynamics on state spaces

We consider the topological entropy of state space and quasi-state space homeomorphisms induced from C*-algebra automorphisms. Our main result asserts that, for automorphisms of separable exact C*-algebras, zero Voiculescu-Brown entropy implies zero topological entropy on the quasi-state space (and also more generally on the entire unit ball of the dual). As an application we obtain a simple description of the topological Pinsker algebra in terms of local Voiculescu-Brown entropy.Comment: 16 pages; some revision; to appear in GAF

Predictors of and changes in older adult loneliness in New Zealand : a thesis presented in partial fulfilment of the requirements for the degree of Master of Arts in Psychology at Massey University, Palmerston North, New Zealand

Objectives: Despite increasing numbers of longitudinal studies addressing loneliness in recent years, the ways in which variables influence changes in loneliness over time are not well understood. The aim of this study is to explore how levels of reported loneliness change over time in a sample of older adult New Zealanders. Method: This study utilises longitudinal data collected for the Health, Work and Retirement Study (HWR) study. Data were collected in 2010, 2012, and 2014 via postal survey. All analyses were conducted with respondents who participated in at least two of the three data waves (N= 2,839). Participants were aged 48 to 85 in 2010. Results: Males were more likely to be lonely, as were those with higher depression scores. High SES, social support, Māori ethnicity, older age and good health were related to lower loneliness levels. Multi-level modelling was used to examine the relationship of predictors to loneliness and changes in loneliness over time. There was a slight reduction in loneliness over time on average, however this decrease was less pronounced for those with higher levels of depression and higher social support. Individuals with activity limitations increased in loneliness over time. An increase in depression over time was related to higher loneliness scores, whereas increases in SES and social support resulted in lower levels of loneliness. Conclusions: Findings are discussed in relation to a model of the development and maintenance of loneliness in older adults. Implications for addressing loneliness in this group will be highlighted