On the conservation of energy: Noether's theorem revisited.

This paper studies the dynamics and conservation of energy. It evaluates the validity of Noether's theorem as a formal argument supporting the law of conservation of energy in physical systems. The analysis examines the role of nonconvexity in energy dynamics. The paper argues that nonconvexity can arise in the presence of catalytic effects or in situations of transitions between multiple regimes. With the introduction of nonconvexity, the analysis relies on a generalized Lagrangian and generalized Hamiltonian. The investigation applies under general conditions, allowing for multiple types of energy with dynamics driven by multiple state variables. Our key result is to show that the conservation of energy (Noether's theorem) holds under convexity but not under nonconvexity. This identifies situations where energy in isolated systems is not necessarily constant over time. By relaxing the law of conservation of energy, our analysis provides new insights into energy dynamics. It offers new directions for scientific inquiries, including improved understanding about the origin of life, the evolution of the early universe and the nature of space and time.

Receptiveness to advice, cognitive ability, and technology adoption☆.

We construct a model of technology adoption with agents differing on two dimensions: their cognitive ability and their receptiveness to advice. While cognitive ability unambiguously speeds adoption, receptiveness to advice may speed adoption for individuals with low cognitive ability, but slow adoption for individuals with high cognitive ability. We conduct economic experiments measuring US farmers' cognitive ability and receptiveness to advice and examine how these characteristics impact their speed of adoption of genetically modified (GM) corn seeds. The empirical analysis shows that early adopters are those who are both quite able cognitively and not receptive to advice.

How should economists model climate? Tipping points and nonlinear dynamics of carbon dioxide concentrations.

Economists modeling climate policy face an array of choices when modeling climate change, including the role of uncertainty/ambiguity, irreversibility, and tipping points. After filtering out estimated cycles due to orbital climate forcing, we use a threshold quantile autoregressive model to characterize anomalies in atmospheric CO2 concentrations. We then test for local instability and tipping points, and we characterize the stationary distribution of anomalies. We find evidence of nonlinear dynamics, tipping points and a non-normal stationary distribution.

Modeling population dynamics: A quantile approach.

The paper investigates the modeling of population dynamics, both conceptually and empirically. It presents a reduced form representation that provides a flexible characterization of population dynamics. It leads to the specification of a threshold quantile autoregression (TQAR) model, which captures nonlinear dynamics by allowing lag effects to vary across quantiles of the distribution as well as with previous population levels. The usefulness of the model is illustrated in an application to the dynamics of lynx population. We find statistical evidence that the quantile autoregression parameters vary across quantiles (thus rejecting the AR model as well as the TAR model) as well as with past populations (thus rejecting the quantile autoregression QAR model). The results document the nature of dynamics and cycle in the lynx population over time. They show how both the period of the cycle and the speed of population adjustment vary with population level and environmental conditions.