Statistical Mechanics of Phase-Space Curves

We study the classical statistical mechanics of a phase-space curve. This unveils a mechanism that, via the associated entropic force, provides us with a simple realization of effects such as confinement, hard core, and asymptotic freedom. Additionally, we obtain negative specific heats, a distinctive feature of self-gravitating systems and negative pressures, typical of dark energy.Comment: 24 pages, 15 figure

3D Effects Of The Entropic Force

This work analyzes the classical statistical mechanics associated to phase-space curves in three dimensions. Special attention is paid to the entropic force. Strange effects like confinement, hard core, and asymptotic freedom are uncovered. Negative specific heats, that were previously seen to emerge in a one-dimensional setting, disappear in 3D, and with them, gravitational effects of the entropic force.Comment: arXiv admin note: substantial text overlap with arXiv:1306.203

Canonical quantization of non-local field equations

We consistently quantize a class of relativistic non-local field equations characterized by a non-local kinetic term in the lagrangian. We solve the classical non-local equations of motion for a scalar field and evaluate the on-shell hamiltonian. The quantization is realized by imposing Heisenberg's equation which leads to the commutator algebra obeyed by the Fourier components of the field. We show that the field operator carries, in general, a reducible representation of the Poincare group. We also consider the Gupta-Bleuler quantization of a non-local gauge field and analyze the propagators and the physical states of the theory.Comment: 18 p., LaTe

Physical peculiarities of divergences emerging in q-deformed statistics

It was found in [Europhysics Letters {\bf 104}, (2013), 60003] that classical Tsallis theory exhibits poles in the partition function ${\cal Z}$ and the mean energy $$. These occur at a countably set of the q-line. We give here, via a simple procedure, a mathematical account of them. Further, by focusing attention upon the pole-physics, we encounter interesting effects. In particular, for the specific heat, we uncover hidden gravitational effects.Comment: 21 pages, 3 figures. Title has changed. Text has change

A Family of unitary higher order equations

A scalar field obeying a Lorentz invariant higher order wave equation, is minimally coupled to the electromagnetic field. The propagator and vertex factors for the Feynman diagrams, are determined. As an example we write down the matrix element for the Compton effect. This matrix element is algebraically reduced to the usual one for a charged Klein-Gordon particle. It is proved that the $n^{th}$ order theory is equivalent to n independent second order theories. It is also shown that the higher order theory is both renormalizable and unitary for arbitrary n.Comment: 17 pages, LaTex, no figure

Interacting social processes on interconnected networks

We propose and study a model for the interplay between two different dynamical processes --one for opinion formation and the other for decision making-- on two interconnected networks $A$ and $B$. The opinion dynamics on network $A$ corresponds to that of the M-model, where the state of each agent can take one of four possible values ($S=-2,-1,1,2$), describing its level of agreement on a given issue. The likelihood to become an extremist ($S=\pm 2$) or a moderate ($S=\pm 1$) is controlled by a reinforcement parameter $r \ge 0$. The decision making dynamics on network $B$ is akin to that of the Abrams-Strogatz model, where agents can be either in favor ($S=+1$) or against ($S=-1$) the issue. The probability that an agent changes its state is proportional to the fraction of neighbors that hold the opposite state raised to a power $\beta$. Starting from a polarized case scenario in which all agents of network $A$ hold positive orientations while all agents of network $B$ have a negative orientation, we explore the conditions under which one of the dynamics prevails over the other, imposing its initial orientation. We find that, for a given value of $\beta$, the two-network system reaches a consensus in the positive state (initial state of network $A$) when the reinforcement overcomes a crossover value $r^*(\beta)$, while a negative consensus happens for $r<r^*(\beta)$. In the $r-\beta$ phase space, the system displays a transition at a critical threshold $\beta_c$, from a coexistence of both orientations for $\beta<\beta_c$ to a dominance of one orientation for $\beta>\beta_c$. We develop an analytical mean-field approach that gives an insight into these regimes and shows that both dynamics are equivalent along the crossover line $(r^*,\beta^*)$.Comment: 25 pages, 6 figure