In the course we will first introduce the basic concepts of percolation, its scaling laws and its fractal subsets like the backbone, the elastic backbone, the shortest path with its perturbations and the distribution of currents. We will also present rigidity percolation, bootstrap percolation and drilling percolation. Particular emphasis will be given to discontinuous percolation like...
Control theory is an important topic for physicists that rarely is covered by standard curricula. In these three sessions, I will introduce the main ideas and discuss basic ideas such as feedback, feedforward, and robustness and how they apply to stochastic thermodynamics.
- Session 1 will introduce control theory as a whole and motivate its interest and value to physicists, both for...
In the last decades thermodynamics have been extended to small (microscopic or nanoscopic) scales, where fluctuations play a major role pushing systems out of equilibrium, and where genuine quantum effects cannot be neglected anymore. Quantum thermodynamics is an interdisciplinary and growing field that places at the intersection of quantum information and non-equilibrium statistical physics....
A bearing is a system of spheres (or disks) in contact. If in a bearing every loop must be even, one can obtain “bearing states”, in which touching spheres roll on each other without slip. We frustrate a system of touching spheres by imposing two different bearing states on opposite sides and search for the configurations of lowest energy dissipation. For Coulomb friction (with random friction...
We study the supercooled dynamics of the Gaussian Core Model in the low- and intermediate-density regimes by means of molecular dynamics simulations. In particular, we discuss the transition from the low-density hard-sphere-like glassy dynamics to the high-density one. The caging mechanism describes the dynamics at low densities well, giving rise to intermittent dynamics. At high densities,...
The use of cognitive assessments aids in identifying notable impairments, especially within cases involving the frontal lobe, as well as instances of neurodegenerative disorders like Alzheimer's, Parkinson's, and semantic dementia, among other pathologies.
This study concentrates on semantic memory, a crucial facet of cognitive storage responsible for integrating language and concepts...
The biodiverse triangle of Santurban and Berlin, in northern Colombia, has been in the center of an environmental conflict since the 90s. Gold mining corporations, national and local governments and its inhabitants are clashing over economic development and the protection of the main source of water for more than 3 million people. Colombian legal framework provides individuals and communities...
The analysis of contagion-diffusion processes in metapopulations is a powerful theoretical tool to study how mobility influences the spread of communicable diseases. Here we address the impact that recurrent patterns of mobility, and the spatial distribution of distinguishable agents, have on the development of epidemics in large urban areas. We incorporate the distinguishable nature of agents...
In this work we present a statistical mechanics perspective for two simple kinetic models in which the exchange rules between an agent pair selected stochastically differ in which, for the first model, the quantity conserved in the exchange is the sum of the respective quantities that the two agents have before and after the exchange, and for the second model the quantity conserved is the...
The kinetic model of opinion formation by Deffuant-Neau-Amblard-Weisbush (DNAW), one of the most well-known in sociophysics, describes the process of opinion formation towards consensus or homogeneous opinions. This is done by considering exchanges of opinion between pairs of agents, in such a way that these exchanges have limited influence as they are confined within a range of opinion and...
The distribution by regions of electoral voting is frequently studied in the sociopolitical field. Making use of the databases on presidential and congressional voting reported by the Registraduria NAcional del Estado Civil (RNEC) in Colombia, by the Servicio Electoral de Chile (SERVEL) and by the Instituto Nacional Electoral (INE) in Mexico, it is found that the votes obtained in properly...
Most stochastic processes are solved by knowing the probability distribution of the process increments or the transition probability distribution that satisfies a Fokker-Planck equation. Also, a rather interesting and known application of stochastic processes is in the Feynman-Kac formula, which presents the equivalence of parabolic partial differential equation problems and stochastic...
Urban mobility is a critical variable in urban planning. Understanding mobility patterns support decision-making processes at the city level. This talk shows how representing the movement flows of people in the city through networks and using concepts and tools derived from statistical physics and complex networks allow us to identify interesting patterns. Some results regarding differences...
Three short stories will be used to illustrate how percolation theory can be used to diagnose and understand some of the urban mobility problems that are faced today by some of the world’s cities. All the stories have in common that they address how the local flows in the roads are organized collectively into a global city flow. The third story characterizes this organization process of...
When a discrete-time process on a network is stochastically brought back from time to time to its starting node, the mean search time needed to reach another node of the network may be significantly decreased. In other cases, however, resetting is detrimental to search. Using the eigenvalues and eigenvectors of the transition matrix defining the process without resetting, we derive a general...
Chess is a board game that demands deep positional understanding from the first move of the opening to the end of the game. Here, we present a method for assessing the true intentions of chess players in their opening move, which is often considered to be the most crucial decision in a match. We use a hidden variables formalism developed for complex networks, and our findings include a study...
In this paper, we explore the reduction of functionality in a complex system as a consequence of cumulative random damage and imperfect reparation, a phenomenon modeled as a dynamical process on networks. We analyze the global characteristics of the diffusive movement of random walkers on networks where the walkers hop considering the capacity of transport of each link. The links are...
A common application of the Ising model is the study of ferromagnetic materials and their properties. One of said properties, M, the magnetization, can be so easily defined that one may wonder if it is possible to come up with an analytical way of estimating its average value. Using the microcanonical framework of counting the different states the system can be in, this work proves a...
Cellular processes are inherently stochastic, leading to protein level variations and gene expression fluctuations known as noise. Accurately understanding how noise spreads within gene networks is vital for creating gene circuits capable of withstanding noise and for comprehending signal reliability in biological networks. However, current models focusing on noise propagation are often...
In molecular dynamics simulations, thermostats are algorithms known for reproducing the canonical or NVT ensemble on a system of particles, i.e., they reproduce a given temperature in the system. In this work, we review a stochastic thermostat algorithm to reproduce Langevin dynamics according to the equation $\dot{v} = \frac{F}{m} - \gamma v + b\xi$ where $F$ is the total external force,...
Thanks to Einstein’s relation, it is known that two-dimensional diffusion coefficients give the amount of area that a particle under Brownian motion can cover in a determined time. In biological sciences, the diffusion coefficient is a relevant parameter to understand the motion of proteins and molecules providing quantitative insights into the mechanical properties of their microenvironment...
In the realm of statistical physics, this study explores the critical properties of the Ising model on two fractal lattices with different Hausdorff dimensions ($d_H \approx 1.892$ and $d_H \approx 1.595$). By employing the Monte Carlo technique and the Metropolis algorithm, a numerical analysis is presented to determine critical temperature values and correlation length functions....
Jigsaw puzzles are a fascinating pastime that has given many hours of fun to people since its first appearance as an educational tool in geography in 1766. Multiple studies on human behavior, the way in which new knowledge is generated, cognitive styles, among others, have been carried out based on the process in which a puzzle is assembled. However, this work proposes a different approach in...
Fluctuation scaling is an emergent property of complex systems that relates the variance ($\Xi$) and the mean ($\Upsilon$) from an empirical data set in the form $\Xi\sim\Upsilon^{\alpha_{TFS}}$, where the dispersion (fluctuation) of the data has been described in terms of $\Xi$. Taking into account the path integral formalism developed by H. Kleinert, we extend the path integral formalism in...
Hereby we investigate the thermalization of a classical harmonic oscillator starting from a micro-canonical ensemble at energy Eo and finishing in a canonical one at temperature T. We derived analytically that the probabilities $P(Q)$ and $P(−Q)$ of gaining or losing a certain amount of heat $Q$ are related as $P(Q)=\exp(-2Q/kT) P(-Q)$, a result we also verified through molecular dynamics...
Granular media consist of a large number of discrete particles interacting mostly through contact forces that, being dissipative, jeopardizes a classical statistical equilibrium approach based on energy. Instead, two independent equilibrium statistical descriptions have been proposed: the Volume Ensemble and the Force Network Ensemble. Hereby, we propose a procedure to join them into a single...
The proof of Liouville's theorem is important in statistical physics because it establishes a fundamental principle in the theory of dynamical systems and statistical thermodynamics. Liouville's theorem states that in a conservative system (where the total energy is conserved), the volume in phase space occupied by a set of initial conditions is also conserved over time. Starting from three...
The idea of a heat engine proposed by thermodynamics has been a great achievement in the development of classical physics. Based on this concept, mesoscopic heat engines were derived, which operate at micro-scales where thermal fluctuations acquire an important role for modeling the system. In consequence, the system must be modeled following a probabilistic point of view, as suggested by...
Manganites consist of an alloy of manganese oxide ($MnO_3$) in conjunction with a rare-earth element (Lanthanum, Strontium, or Germanium). a particular case is Lanthanum manganite doped with praseodymium (LPCMO). This material holds significant interest due to their magnetic phase transitions occurring below temperatures of 130 K. One of the phenomena observed is the coexistence of...
Verbal fluency tests provide some insight into memory information and retrieval processes. These tests can be represented as a complex network, where the nodes are the words of the fluency test and the links between nodes are the semantic relationship of the words. The complex network formed in this way has been called a “semantic network”. To decipher the search mechanisms used by the brain...
The universe lives on a Gravitational Wave Background (GWB). This GWB is extra energy that is not contained in Einstein's equations, and new models was developed to explain the accelerating expansion of the universe where a GWB is incorporated into Einstein's equations.
In this talk, we study this new paradigm: due to GWB, quantum particles cannot follow geodesics, but rather stochastic...
The formation of traffic bottlenecks in main roads is one of the most common causes of vehicular congestion, having a bigger impact in cities with main roads consisting of few lanes i.e. 2 or 3 lanes. A traffic bottleneck creates a challenge for those drivers who are in the congested lane since they must find a way to change lanes in order to surpass the bottleneck. In this scenario the best...
MnAlCu systems has shown enormous potential as permanent magnets due to their magnetic properties, which is why their characterization study has been carried out. During this research, uniaxial anisotropy was discover using FORC diagrams, which showed different uncentered boomerang shapes that varied depending on the percentage of doping. Furthermore, in order to understand their domains...
Information engines are a modern realization of the Maxwell-demon thought experiment. They exploit “favorable fluctuations” of a heat bath to generate work, at the cost of dissipation in a measuring device. Experimental tests of these engines require accurate measurements and fast feedback control. We designed a simple information engine using optical tweezers and feedback to raise a...
The simulation of stochastic systems is a valuable tool to investigate a broad range of topics, from atomistic simulations of colloidal systems and magnetic materials to the simulation of interest rates and derivatives in mathematical finance. In most cases, these systems are simulated by integrating the corresponding stochastic differential equations (SDEs) via the Euler-Maruyama, Milstein or...
A modification of the classical Szilard engine is presented, where pores have been drilled on the piston. This change allows for the traversal of the particle from one side of the piston to the other, making it unnecessary to remove the piston from the engine, nor measure the position of the particle for the engine to do work. The dissipation on energy occurs when the mass over which the...
When a system deviates from equilibrium, it is possible to manipulate and control it to drive it towards equilibrium within a finite time $t_f$, even reducing its natural relaxation time scale $\tau_{relax}$. Although numerous theoretical and experimental studies have explored these shortcut protocols, few have yielded analytical results for the probability distribution of work, heat and...
Strongly electron-correlated materials provide a rich platform for exploring the underpinnings of fundamental physics. These systems are characterized by a complex energy landscape, originating from the interplay of competing phases, which manifests in diverse phenomena including metal-insulator transitions, multiple magnetic transitions, and structural phase transitions. In some instances,...
In this work, the ferromagnetic phase transition in a monolayer of chromium triiodide (CrI3) was examined. Employing a microcanonical ensemble approach, entropy was evaluated as a function of internal energy and magnetization was calculated with respect to energy across various spin configurations. In this way, a methodology was found to observe phase transitions using thermodynamic quantities...
Using the mean-field renormalization group method (MFRG) and starting from the Ising Hamiltonian, magnetic phase diagrams were successfully reproduced in various systems composed of different types of magnetic atoms, such as FeMnAl, FeNiMn, and FeAl alloys. Quadratic errors we obtained below 0.016, and a preliminary approximation of the binding energy between atoms of this type was achieved....
In this document, we study the planar metallic layers at a constant voltage from the point of view of statistical mechanics and electrostatics. We use molecular dynamics simulations to find the system's positional correlation functions and velocity distributions by modeling it as a two-dimensional Coulomb plasma in the liquid phase. Alternatively, the surface charge density is calculated by...
More than 150 years ago, James Clerk Maxwell introduced a famous thought experiment, where a little intelligent being (the “demon”) defies the second law of thermodynamics by controlling a tiny door between two chambers with gases at different temperatures. Maxwell’s demon represented a cornerstone in the development thermodynamics of feedback control, and has attracted renewed attention...
In quantum thermodynamics, fluctuation theorems provide a way for the quantification of irreversibility of single trajectories. In this work we propose a description of the dynamics of single trajectories based on an M-parametrization of unravellings of the master equation for a system coupled to its environment. We identify the measurable components of the entropy, and show ways to measure...
An important task in quantum thermodynamics consists of the characterization of work and heat in the quantum domain. A common approach to this problem, known as the two-point measurement (TPM) scheme, consists of performing two projective energy measurements at the beginning and at the end of a given evolution protocol. Although its importance for the development of the understanding of work...
We study the non-equilibrium dynamics for no-fusion and fusion events in a Dyson gas of $N$ charged particles interacting through a logarithmic Coulomb potential surrounded by a thermal bath at a reduced temperature $\beta=q_0^2/(k_BT)$, where $q_0$ is the charge per particle and $T$ is temperature of the bath. First, we characterize the relaxation-time, $\tau$, in the regime for no-fusion...
Basic methods of statistical physics have proven extremely useful in the modelling of enzyme dynamics, but now the concepts of statistical physics have become important tools in many areas of systems biology, such as protein folding, site search on DNA, gene regulation, evolutionary dynamics or information processing. I will present an overview of the use of the concepts (more than the...
Cryo-electron microscopy (cryo-EM) has recently become a leading method for obtaining high-resolution structures of biological macromolecules. However, cryo-EM is limited to biomolecular samples with low conformational heterogeneity, where most conformations can be well-sampled at various projection angles.
While cryo-EM provides single-molecule data for heterogeneous molecules, most existing...
The Tsallis’ non-extensive statistical mechanics is a generalized framework for describing complex systems where ergodicity (and statistical equilibrium as its macroscopic manifestation) is just one of the dynamic possibilities of microscopical mixing. In practical manners, the generalization from Tsallis’ theory introduces a non-extensive entropic functional Sq through the q-index, which...
Ab initio metadynamics enables the extraction of free energy landscapes with the precision of first-principles electronic structure methods. We developed and used an interface between the PLUMED and ASE codes to estimate the free energy of Ag5 and Ag6 clusters at 10, 100, and 300 K with the radius of gyration and coordination number as collective variables [1]. We find that Ag6 is the smallest...
We describe the steady state of the annihilation process of a one-dimensional system of two initially separated reactants A and B. The parameters that define the dynamical behavior of the system are the diffusion constant, the reaction rate, and the deposition rate. Depending on the ratio between those parameters, the system exhibits a crossover between a diffusion-limited (DL) regime and a...
In the conventional quantum mechanics of conserved systems, Hamiltonian is assumed to be a Hermitian operator. However, when it comes to quantum systems in presence of dissipation and/or noise, including open quantum optical systems, the strict hermiticity requirement is no longer necessary. In fact, it can be substantially relaxed: the non-Hermitian part of a Hamiltonian is allowed, in order...
