This undergraduate thesis work consists in a deepth study of the Einstein's field equation in general relativity over a thermodynamic perspective. We study the local Minkwoski space-time $(\mathbb{R}⁴,\eta_{\mu\nu})$ evoking the usual causal horizon $t² = |\vec{x}|²$ as a thermal wall and space-like events as a thermodynamic system. In that sense, heat $Q$ is naturally the flux of energy...
The equilibration protocols have been extensively studied but few analytical solutions have been found. In this work, we have proposed a protocol that have analytical solutions for the relevant thermodynamics quantities and exhibits an universal behavior for short time duration.
We study the time-evolution from an initial state to an equilibrium state for a 2D-Dyson gas of $N$ charged particles interacting through a 2D-logarithmic Coulomb potential surrounded by a thermal bath at a reduced temperature $\beta=q^2_0/(k_BT)$, with $q_0$ the charge per particle, $T$ the temperature of the bath and $k_B$ the Boltzmann's constant, for $\beta$ in range $[0.1,4.0]$. We...
Self-organized criticality is a dynamical system property where, without external tuning, a system naturally evolves towards its critical state, characterized by scale-invariant patterns and power-law distributions. In this paper, we explored a self-organized critical dynamic on the Sierpinski carpet lattice, a scale-invariant structure whose dimension is defined as a power-law with a...
The evolution of an incompressible and inviscid fluid is determined by the Euler equations, which are nonlinear and nonlocal partial differential equations for the fluid velocity field. Although many properties and features of Euler equations are well known, it is not known if the velocity can or cannot develop a singularity in finite time in a three-dimensional space (3D). It is presented a...
