On the Geometry and Entropy of Non-Hamiltonian Phase Space

We analyze the equilibrium statistical mechanics of canonical, non-canonical and non-Hamiltonian equations of motion by throwing light into the peculiar geometric structure of phase space. Some fundamental issues regarding time translation and phase space measure are clarified. In particular, we emphasize that a phase space measure should be defined by means of the Jacobian of the transformation between different types of coordinates since such a determinant is different from zero in the non-canonical case even if the phase space compressibility is null. Instead, the Jacobian determinant associated with phase space flows is unity whenever non-canonical coordinates lead to a vanishing compressibility, so that its use in order to define a measure may not be always correct. To better illustrate this point, we derive a mathematical condition for defining non-Hamiltonian phase space flows with zero compressibility. The Jacobian determinant associated with time evolution in phase space is altogether useful for analyzing time translation invariance. The proper definition of a phase space measure is particularly important when defining the entropy functional in the canonical, non-canonical, and non-Hamiltonian cases. We show how the use of relative entropies can circumvent some subtle problems that are encountered when dealing with continuous probability distributions and phase space measures. Finally, a maximum (relative) entropy principle is formulated for non-canonical and non-Hamiltonian phase space flows.Comment: revised introductio

Day occupation is associated with psychopathology for adolescents and young adults with Down syndrome

Background: Young adults with Down syndrome experience increased rates of emotional and behavioural problems compared with the general population. Most adolescents with Down syndrome living in Western Australia participate in sheltered employment as their main day occupation. Relationship between day occupation and changes in behaviour has not been examined. Therefore, the aim of this research was to explore any relationship between post school day occupations and changes in the young person’s behaviour. Methods: The Down syndrome Needs Opinion Wishes database was used for case ascertainment of young adults aged 15 to 32 years with Down syndrome. Families of 118 young people in this population-based database completed questionnaires in 2004, 2009 and 2011. The questionnaires addressed both young person characteristics such as age, gender, presence of impairments, behaviour, functioning in activities of daily living, and family characteristics such as income and family functioning. Post-school day occupations in which the young people were participating included open and sheltered employment, training and day recreation programs. Change in behaviour of young adults who remained in the same post-school day occupation from 2009 to 2011 (n = 103) were examined in a linear regression model adjusting for confounding variables including age, gender, prior functioning and behaviour in 2004 and family income.Results: In comparison to those young adults attending open employment from 2009 to 2011, those attending day recreation programs were reported to experience worsening in behaviour both in the unadjusted (effect size -0.14, 95% CI -0.24, -0.05) and adjusted models (effect size -0.15, 95% CI -0.29, -0.01). Conclusions: We found that the behaviour of those participating in open employment improved compared to those attending other day occupations. Further examination of the direction of this association is required

Multiscale Modeling Examples: New Polyelectrolyte Nanocomposite Membranes for Perspective Fuel Cells and Flow Batteries

Renewable energy production from fuel cells and energy storage in flow batteries are becoming increasingly important in the modern energy transition. Both batteries use polyelectrolyte membranes (PEMs) to allow proton transport. In this chapter, both PEMs and PEMs-based nanocomposites have been discussed using various simulational approaches. A coarse-grained model of a Nafion film capped by the substrates with variable wettability has been used to simulate nanocomposites of PEMs by classical molecular-dynamics (MD) method. Classical MD modeling results have also been reviewed for a PEM-graphene oxide nanocomposite internal structure and dynamics. Ab-initio simulations have been implemented to describe the proton transfer pathways in anhydrous PEMs. Finally, the large-scale mesoscopic simulations have been introduced to shed light on the water domain features present in the hydrated PEMs. A brief description of polybenzimidazole membrane as electrolyte and Ionic Liquids as dopants for fuel cells is also presented