Making Reflective Equlibrium Precise: A Formal Model

Reflective equilibrium (RE) is often regarded as a powerful method in ethics, logic, and even philosophy in general. Despite this popularity, characterizations of the method have been fairly vague and unspecific so far. It thus may be doubted whether RE is more than a jumble of appealing but ultimately sketchy ideas that cannot be spelled out consistently. In this paper, we dispel such doubts by devising a formal model of RE. The model contains as components the agent’s commitments and a theory that tries to systematize the commitments. It yields a precise picture of how the commitments and the theory are adjusted to each other. The model differentiates between equilibrium as a target state and the dynamic equilibration process. First solutions to the model, obtained by computer simulation, show that the method allows for consistent specification and that the model’s implications are plausible in view of expectations on RE. In particular, the mutual adjustment of commitments and theory can improve one’s commitments, as proponents of RE have suggested. We argue that our model is fruitful not only because it points to issues that need to be dealt with for a better understanding of RE, but also because it provides the means to address these issues.

Toward a relativistic microscopic substantiation of thermodynamics: the equilibration mechanism

The microscopic deterministic mechanism of the irreversible equilibration process in a relativistic classical system of interacting particles has been established.

Curved space equilibration versus flat space thermalization: A short review

We discuss equilibration process in expanding Universes as compared to the thermalization process in Minkowski spacetime. The final goal is to answer the following question: Is the equilibrium reached before the rapid expansion stops and quantum effects have a negligible effect on the background geometry or stress–energy fluxes in a highly curved early Universe have strong effects on the expansion rate and the equilibrium is reached only after the drastic decrease of the spacetime curvature? We argue that consideration of more generic non-invariant states in theories with invariant actions is a necessary ingredient to understand quantum field dynamics in strongly curved backgrounds. We are talking about such states in which correlation functions are not functions of such isometry invariants as geodesic distances, while having correct UV behavior. The reason to consider such states is the presence of IR secular memory effects for generic time-dependent backgrounds, which are totally absent in equilibrium. These effects strongly affect the destiny of observables in highly curved spacetimes.

Collisionless relaxation of a disequilibrated current sheet and implications for bifurcated structures

Current sheets are ubiquitous plasma structures that play the crucial role of being energy sources for various magnetic phenomena. Although a plethora of current sheet equilibrium solutions have been found, the collisionless process through which a disequilibrated current sheet relaxes or equilibrates remains largely unknown. Here we show, through analyses of phase-space distributions of single-particle orbit classes and particle-in-cell simulations, that collisionless transitions among the orbit classes are responsible for this process. Bifurcated current sheets, which are readily observed in geospace but whose origins remain controversial, are shown to naturally arise from the equilibration process and thus are likely to be the underlying structures in various phenomena; comparisons of spacecraft observations to particle-in-cell simulations support this fact. The bearing of this result on previous explanations of bifurcated structures is also discussed.

Collisionless Relaxation of a Disequilibrated Current Sheet and Implications for Bifurcated Structures

Current sheets are ubiquitous plasma structures that play the crucial role of being energy sources for various magnetic phenomena. Although a plethora of current sheet equilibrium solutions have been found, the collisionless process through which a disequilibrated current sheet relaxes or equilibrates remains largely unknown. Here we show, through analyses of phase-space distributions of single-particle orbit classes and particle-in-cell simulations, that collisionless transitions among the orbit classes are responsible for this process. Bifurcated current sheets, which are readily observed in geospace but whose origins remain controversial, are shown to naturally arise from the equilibration process and thus are likely to be the underlying structures in various phenomena; comparisons of spacecraft observations to particle-in-cell simulations support this fact. The bearing of this result on previous explanations of bifurcated structures is also discussed.

Non-equilibrium response and slow equilibration in hard disk systems

The relaxation from a non-equilibrium state to the equilibrium depends on the methodologies and initial conditions. To investigate the microscopic mechanisms of equilibration systematically, we focus on the non-equilibrium response during the equilibration process induced by a disturbance of the homogeneous expansion of the simple hard disk systems. Large scale simulations by event-driven molecular dynamics revealed that an anomalous slow equilibration toward the liquid states emerges when starting from the co-existence phase. The origin of the slow decay mechanism is investigated using the probability distribution of local density and orientational order parameter.Their inhomogeneities seem to cause the anomalous slow equilibration.

Controlling the All-trans Stereochemistry in Liquid Crystalline 4,4′-Dialkyl-[1,1′-bicyclohexyl] Compounds

A good part of today’s liquid crystals (LCs) for display applications are derived from the Darzens–Nenitzescu reaction which, in a one-pot-process, yields 1,4-trans-acylphenylcyclohexanes from acid chlorides, benzene, and cyclohexene. A mechanism for this process is proposed based on quantum-chemical computations. The products of this reaction can be further elaborated to all-trans-4,4′-disubstituted-[1,1′-bicyclohexane] compounds, essential components in almost all fast switching LC-mixtures. An equilibration process involving carbo­cations is used to control the diastereomer distribution.

Potentially Toxic Element Availability and Risk Assessment of Cadmium Dietary Exposure after Repeated Croppings of Brassica juncea in a Contaminated Agricultural Soil

Phytoextraction of potentially toxic elements (PTEs) is eco-friendly and cost-effective for remediating agricultural contaminated soils, but plants can only take up bioavailable forms of PTEs, thus meaning that bioavailability is the key for the feasibility of this technique. With the aims to assess the phytoextraction efficiency on an agricultural soil contaminated by Cr, Zn, Cd, and Pb and the changes induced by plants in PTE bioavailability and in human health risk due to dietary exposure, in this work we carried out a mesocosm experiment with three successive croppings of Brassica juncea, each followed by Rocket salad as bioindicator. Brassica juncea extracted more Zn and Cd than Cr and Pb, significantly reducing, after three repeated croppings, the bioavailable element concentrations in soil as a result of plant uptake and soil pH changes. For Cd, this reduction did not bring the bioavailable amounts obtained by soil extraction with NH4NO3 below the trigger value of 0.1 mg kg−1 set by some European countries. Nevertheless, the Hazard Quotient for Cd in Rocket salad decreased across three repeated croppings of Brassica juncea. This indicated the beginning of a re-equilibration process between soil PTE forms of different bioavailability, that are in a dynamic equilibrium, thus stressing the need to monitor the possible regeneration of the most readily bioavailable pool.

Excitation energy transfer and equilibration process in LHCII studied by multidimensional electronic spectroscopy

Light-harvesting complex II (LHCII) – the light-harvesting antenna of Photosystem II – is a naturally abundant system that plays an important role in photosynthesis. In this study, we present a phenomenological analysis of the excitonic energy transfer in LHCII using ultrafast two-dimensional electronic spectroscopy, that we find compares well with previous theoretical and experimental results.