Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: Dirac field

We derive the general exact forms of the Wigner function, of mean values of conserved currents, of the spin density matrix, of the spin polarization vector and of the distribution function of massless particles for the free Dirac field at global thermodynamic equilibrium with rotation and acceleration, extending our previous results obtained for the scalar field. The solutions are obtained by means of an iterative method and analytic continuation, which lead to formal series in thermal vorticity. In order to obtain finite values, we extend to the fermionic case the method of analytic distillation introduced for bosonic series. The obtained mean values of the stress-energy tensor, vector and axial currents for the massless Dirac field are in agreement with known analytic results in the special cases of pure acceleration and pure rotation. By using this approach, we obtain new expressions of the currents for the more general case of combined rotation and acceleration and, in the pure acceleration case, we demonstrate that they must vanish at the Unruh temperature.

The effect of microbial selection on the occurrence-abundance patterns of microbiomes

Theoretical models are useful to investigate the drivers of community dynamics. Notable are models that consider the events of death, birth, and immigration of individuals assuming they only depend on their abundance — thus, all types share the same parameters. The community level expectations arising from these simple models and their agreement to empirical data have been discussed extensively, often suggesting that in nature, rates might indeed be neutral or their differences not important. But, how robust are these model predictions to type-specific rates? And, what are the consequences at the level of types? Here, we address these questions moving from simple to diverse communities. For this, we build a model where types are differently adapted to the environment. We adapt a computational method from the literature to compute equilibrium distributions of the abundance. Then, we look into the occurrence-abundance pattern often reported in microbial communities. We observe that large immigration and biodiversity — common in microbial systems — lead to such patterns, regardless of whether the rates are neutral or non-neutral. We conclude by discussing the implications to interpret and test empirical data.

An energy and momentum conserving collisional bracket for the guiding-centre Vlasov–Maxwell–Landau model

This paper proposes a metric bracket for representing Coulomb collisions in the so-called guiding-centre Vlasov–Maxwell–Landau model. The bracket is manufactured to preserve the same energy and momentum functionals as does the Vlasov–Maxwell part and to simultaneously satisfy a revised version of the H-theorem, where the equilibrium distributions with respect to collisional dynamics are identified as Maxwellians. This is achieved by exploiting the special projective nature of the Landau collision operator and the simple form of the system's momentum functional. A discussion regarding a possible extension of the results to electromagnetic drift-kinetic and gyrokinetic systems is included. We anticipate that energy conservation and entropy dissipation can always be manufactured whereas guaranteeing momentum conservation is a delicate matter yet to be resolved.

Fingerprints of nonequilibrium stationary distributions in dispersion relations

Distributions different from those predicted by equilibrium statistical mechanics are commonplace in a number of physical situations, such as plasmas and self-gravitating systems. The best strategy for probing these distributions and unavailing their origins consists in combining theoretical knowledge with experiments, involving both direct and indirect measurements, as those associated with dispersion relations. This paper addresses, in a quite general context, the signature of nonequilibrium distributions in dispersion relations. We consider the very general scenario of distributions corresponding to a superposition of equilibrium distributions, that are well-suited for systems exhibiting only local equilibrium, and discuss the general context of systems obeying the combination of the Schrödinger and Poisson equations, while allowing the Planck’s constant to smoothly go to zero, yielding the classical kinetic regime. Examples of media where this approach is applicable are plasmas, gravitational systems, and optical molasses. We analyse in more depth the case of classical dispersion relations for a pair plasma. We also discuss a possible experimental setup, based on spectroscopic methods, to directly observe these classes of distributions.

Molecular Systems Predict Equilibrium Distributions of Phenotype Diversity Available for Selection

Two long-standing challenges in theoretical population genetics and evolution are predicting the distribution of phenotype diversity generated by mutation and available for selection and determining the interaction of mutation, selection, and drift to characterize evolutionary equilibria and dynamics. More fundamental for enabling such predictions is the current inability to causally link population genetic parameters, selection and mutation, to the underlying molecular parameters, kinetic and thermodynamic. Such predictions would also have implications for understanding cryptic genetic variation and the role of phenotypic robustness. Here we provide a new theoretical framework for addressing these challenges. It is built on Systems Design Space methods that relate system phenotypes to genetically-determined parameters and environmentally-determined variables. These methods, based on the foundation of biochemical kinetics and the deconstruction of complex systems into rigorously defined biochemical phenotypes, provide several innovations that automate (1) enumeration of the phenotypic repertoire without knowledge of kinetic parameter values, (2) representation of phenotypic regions and their relationships in a System Design Space, and (3) prediction of values for kinetic parameters, concentrations, fluxes and global tolerances for each phenotype. We now show that these methods also automate prediction of phenotype-specific mutation rate constants and equilibrium distributions of phenotype diversity in populations undergoing steady-state exponential growth. We introduce this theoretical framework in the context of a case study involving a small molecular system, a primordial circadian clock, compare and contrast this framework with other approaches in theoretical population genetics, and discuss experimental challenges for testing predictions.