Statistical mechanics of ecological systems: Neutral theory and beyond

Statistical Mechanics of Ecological Systems: Neutral Theory and Beyond

Sandro Azaele1,∗, Samir Suweis2,∗, Jacopo Grilli, Igor Volkov, Jayanth R. Banavar, Amos Maritan 1 Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom. 2 Dipartimento di Fisica ‘G. Galilei’ & CNISM, INFN, Università di Padova, Via Marzolo 8, 35131 Padova, Italy. 3 Department of Ecology and Evolution, University of Chicago, 1101 East 57th S...

Number theory, dynamical systems and statistical mechanics

We shortly review recent work interpreting the quotient ζ(s− 1)/ζ(s) of Riemann zeta functions as a dynamical zeta function. The corresponding interaction function (Fourier transform of the energy) has been shown to be ferromagnetic, i.e. positive. On the additive group Gk := (Z/2Z), with Z/2Z = ({0, 1},+). we set inductively h0 := 1, hk+1(σ, 0) := hk(σ) and hk+1(σ, 1) := hk(σ) + hk(1− σ), (1) ...

Quantum and statistical mechanics in open systems: theory and examples

Statistical Mechanics and Information Theory

Definition 1 (Spin Excess) For a system with N particles with spins ±m, the spin excess is given by how many particles more than N/2 have spin +m, i.e. S = N↑ − N2 where N↑ is the number of particles with spin +m. From Definition 1 and Equation (1) it follows that the total magnetic moment is given by M = 2mS. Theoretically, one could calculate the system’s magnetic moment at some point in time...

Statistical mechanics unifies different ecological patterns.

Recently there has been growing interest in the use of maximum relative entropy (MaxREnt) as a tool for statistical inference in ecology. In contrast, here we propose MaxREnt as a tool for applying statistical mechanics to ecology. We use MaxREnt to explain and predict species abundance patterns in ecological communities in terms of the most probable behaviour under given environmental constrai...