arXiv subjects

VS Morales-Salgado

Publications and source records attributed to VS Morales-Salgado.

7 recordsLinked to original sources

arXiv2026

Towards a Framework for Social Mechanics

Social physics explores the possibility that mathematical structures developed in physics may provide useful descriptions of certain social phenomena. In this work, we propose an effective mechanical framework for modelling social change in terms of positions in a space of social stances, together with concepts analogous to motion, inertia, interaction, and force. A central feature of the framework is the introduction of position-dependent inertial responses, allowing susceptibility to social change to vary across stance-space. Within this setting, we investigate deterministic and stochastic models of social evolution, including free motion, effective interactions, and diffusion-driven dynamics. We also discuss Lagrangian and Hamiltonian formulations associated with the proposed framework. As an illustrative application, we model partisan preference distributions in United States presidential elections through effective drift and diffusion processes. The framework is intended as a phenomenological and exploratory approach to social dynamics rather than as a fundamental description of human behaviour.

physics.soc-ph↗

arXiv2026

Ideal Social Gas: Emergent Thermodynamic Observables in an Effective Model of Social Dynamics

This work continues the one commenced in \cite{m24}, where the key idea is that individual stances on a social matter can be modeled as positions of particles in physics. Here, we develop an effective thermodynamic framework for the statistical description of collective social systems based on a mechanical representation of individual stances. In this approach, each individual is modeled as a point-like particle evolving in an abstract stance-space, where the dynamics are characterized by position-dependent inertial response functions. The resulting many-particle system is treated within an equilibrium statistical description analogous to the canonical ensemble of statistical mechanics. Using this framework, we derive the corresponding partition function and introduce emergent macroscopic observables analogous to pressure, volume and temperature, interpreted here as collective statistical properties of the social system. For a particular class of position-dependent mass functions, the resulting equation of state acquires an ideal-gas-like form, suggesting a degree of macroscopic universality despite microscopic heterogeneity among individuals. The formalism is further extended to open social systems through the introduction of a chemical potential associated with population exchange among social groups. This extension naturally allows the treatment of variable particle number and multispecies social configurations within the same equilibrium framework. The present work is intended as an exploratory phenomenological contribution to sociophysics and complex systems research, aimed at investigating whether collective social behavior may admit effective macroscopic statistical descriptions analogous to those encountered in statistical physics.

physics.soc-ph↗

arXiv2026

Synthetic Dynamics

This work reflects on mechanics as an epistemological framework on the state of a physical system to regard dynamics as the distribution of mechanical properties over spacetime coordinates. The resulting distribution is taken to be the partition function of the relevant physical quantities over a spacetime parametrized by coordinates. The partition yields a probabilistic interpretation that, based on Feynman's path integral formulation, leads to a dynamical law that generalizes the Schrödinger equation. A variety of systems can be put into the form proposed here, including particles in potentials, as well as matter and interaction fields. The main advantage of the proposed framework is that it presents the space of properties separately from that of the space of coordinates, whereas the dynamical law can be interpreted as the equation of two differential structures, one from each of these spaces. The resulting framework shows possibilities to further study physical quantities that relate directly to the spacetime coordinates, whose dynamics is best described in thermodynamical, rather than Hamiltonian, terms. A notable example is the theory of general relativity, in which the case of a scalar field in a Robertson-Walker metric is explored.

physics.gen-ph↗

arXiv2018

Coherent states for the supersymmetric partners of the truncated oscillator

We build the coherent states for a family of solvable singular Schrödinger Hamiltonians obtained through supersymmetric quantum mechanics from the truncated oscillator. The main feature of such systems is the fact that their eigenfunctions are not completely connected by their natural ladder operators. We find a definition that behaves appropriately in the complete Hilbert space of the system, through linearised ladder operators. In doing so, we study basic properties of such states like continuity in the complex parameter, resolution of the identity, probability density, time evolution and possibility of entanglement.

math-ph↗

arXiv2017

Higher Order Supersymmetric Truncated Oscillators

We study the supersymmetric partners of the harmonic oscillator with an infinite potential barrier at the origin and obtain the conditions under which it is possible to add levels to the energy spectrum of these systems. It is found that instead of the usual rule for non-singular potentials, where the order of the transformation corresponds to the maximum number of levels which can be added, now it is the integer part of half the order of the transformation which gives the maximum number of levels to be created.

math-ph↗

arXiv2016

SUSY partners of the truncated oscillator, Painlevé transcendents and Bäcklund transformations

In this work the supersymmetric technique is applied to the truncated oscillator to generate Hamiltonians ruled by second and third-order polynomial Heisenberg algebras, which are connected to the Painlevé IV and Painlevé V equations respectively. The aforementioned connection is exploited to produce particular solutions to both non-linear differential equations and the Bäcklund transformations relating them.

math-ph↗

arXiv2013

Supersymmetric partners of the harmonic oscillator with an infinite potential barrier

Supersymmetry transformations of first and second order are used to generate Hamiltonians with known spectra departing from the harmonic oscillator with an infinite potential barrier. It is studied also the way in which the eigenfunctions of the initial Hamiltonian are transformed. The first and certain second order supersymmetric partners of the initial Hamiltonian possess third-order differential ladder operators. Since systems with this kind of operators are linked with the Painlevé IV equation, several solutions of this non-linear second-order differential equation will be simply found.

math-ph↗