arXiv subjects

André M. Timpanaro

Publications and source records attributed to André M. Timpanaro.

12 recordsLinked to original sources

arXiv2026

A family of thermodynamic uncertainty relations valid for general fluctuation theorems

Thermodynamic Uncertainty Relations (TURs) are relations that establish lower bounds for the relative fluctuations of thermodynamic quantities in terms of the statistics of the associated entropy production. In this work we derive a family of TURs that explores higher order moments of the entropy production and is valid in any situation a Fluctuation Theorem holds. The resulting bound holds in both classical and quantum regimes and can always be saturated. These TURs are shown in action for a two level system weakly coupled to a bath undergoing a non time-symmetric drive, where we can use the Tasaki-Crooks fluctuation theorem. Finally, we draw a connection between our TURs and the existence of correlations between the entropy production and the thermodynamic quantity under consideration.

cond-mat.stat-mech↗

arXiv2026

Tightening the thermodynamic uncertainty relations with null-entropy events: What we learn when nothing happens

Fluctuation theorems establish that thermodynamic processes at the microscale can occasionally result in negative entropy production. At the microscale, another distinct possibility becomes more likely: processes in which no entropy is produced overall. In this work, we explore the constraints imposed by such null-entropy events on the fluctuations of thermodynamic currents. By incorporating the probability of null-entropy events, we obtain tighter bounds on finite-time thermodynamic uncertainty relations derived from fluctuation theorems. We validate this framework using an example of a qudit SWAP engine.

cond-mat.stat-mech↗

arXiv2026

Emergence of opinion splits in the Sznajd model with latency

In the modelling of social systems, opinion latency is the idea that once an agent changes its opinion, there will be a period of time where it is immune to other changes. When added to the voter model this leads to a situation where no matter how low the latency is or how many opinions are considered, all opinions end up in a coexistence where they are equally represented. In this work, we examine what happens when latency is added to the Sznajd model. What we find is that for low latency, the model behaves roughly like it does in the absence of latency, where one opinion will always eventually dominate. For high latency, the possibility for a symmetric coexistence of 2 opinions arises, but contrary to the voter model, a coexistence of more than 2 opinions is never stable. We provide evidence of this phenomenon with computer simulations of the model in Barabási-Albert networks, together with a mean field treatment that is able to capture the observed behavior. We argue that this could hint at an explanation for the prevalence of two opinion splits in the real world.

physics.soc-ph↗

arXiv2021

A convex analysis approach to tight expectation inequalities

In this work, we investigate the question of how knowledge about expectations $\mathbb{E}(f_i(X))$ of a random vector $X$ translate into inequalities for $\mathbb{E}(g(X))$ for given functions $f_i$, $g$ and a random vector $X$ whose support is contained in some set $S\subseteq \mathbb{R}^n$. We show that there is a connection between the problem of obtaining tight expectation inequalities in this context and properties of convex hulls, allowing us to rewrite it as an optimization problem. The results of these optimization problems not only arrive at sharp bounds for $\mathbb{E}(g(X))$ but in some cases also yield discrete probability measures where equality holds. We develop an analytical approach that is particularly suited for studying the Jensen gap problem when the known information are the average and variance, as well as a numerical approach for the general case, that reduces the problem to a convex optimization; which in a sense extends known results about the moment problem.

math.PR↗

arXiv2020

Joint fluctuation theorems for sequential heat exchange

We study the statistics of heat exchange of a quantum system that collides sequentially with an arbitrary number of ancillas. This can describe, for instance, an accelerated particle going through a bubble chamber. Unlike other approaches in the literature, our focus is on the \emph{joint} probability distribution that heat $Q_1$ is exchanged with ancilla 1, heat $Q_2$ is exchanged with ancilla 2, and so on. This allows one to address questions concerning the correlations between the collisional events. The joint distribution is found to satisfy a Fluctuation theorem of the Jarzynski-Wójcik type. Rather surprisingly, this fluctuation theorem links the statistics of multiple collisions with that of independent single collisions, even though the heat exchanges are statistically correlated.

quant-ph↗

arXiv2019

Thermodynamic uncertainty relations from exchange fluctuation theorems

Thermodynamic uncertainty relations (TURs) place strict bounds on the fluctuations of thermodynamic quantities in terms of the associated entropy production. In this work we identify the tightest (and saturable) matrix-valued TUR that can be derived from the exchange fluctuation theorems describing the statistics of heat and particle flow between multiple systems. Our result holds for both quantum and classical systems, undergoing general non-Markovian and non-stationary processes. Moreover, it provides bounds not only for the variances, but also for the correlations between thermodynamic quantities. To demonstrate the relevance of TURs to the design of nanoscale machines, we consider the operation of a two-qubit SWAP engine undergoing an Otto cycle and show how our results can be used to place strict bounds on the correlations between heat and work.

quant-ph↗

arXiv2019

Dynamical chaotic phases and constrained quantum dynamics

In classical mechanics, external constraints on the dynamical variables can be easily implemented within the Lagrangian formulation. Conversely, the extension of this idea to the quantum realm, which dates back to Dirac, has proven notoriously difficult due to the noncommutativity of observables. Motivated by recent progress in the experimental control of quantum systems, we propose a framework for the implementation of quantum constraints based on the idea of work protocols, which are dynamically engineered to enforce the constraints. As a proof of principle, we consider the dynamical mean-field approach of the many-body quantum spherical model, which takes the form of a quantum harmonic oscillator plus constraints on the first and second moments of one of its quadratures. The constraints of the model are implemented by the combination of two work protocols, coupling together the first and second moments of the quadrature operators. We find that such constraints affect the equations of motion in a highly nontrivial way, inducing nonlinear behavior and even classical chaos. Interestingly, Gaussianity is preserved at all times. A discussion concerning the robustness of this approach to possible experimental errors is also presented.

quant-ph↗

arXiv2017

Diversity and Disorder in the Voter Model with Delays

In this work, we investigate interactions that simultaneously order a system locally, while keeping it globally disordered. The study is done in the context of the emergence of diversity in opinion propagation models with interactions rooted in conformity, but some suggestions on how this could be extended to other topics (like ecology and neuroscience) are also made. We do this by introducing a generic modification that can be added to different opinion propagation models (and other agent based models) and that seems to introduce a global tendency towards diversity without leading the system to a frozen state, even in the absence of thermal noises, contrarian agents or cyclic interactions. This modification consists of effectively introducing a relaxation period right after an agent changes its state, during which it cannot change its state again. We tested this modification for the voter model in a square lattice and verified that in the thermodynamic limit, the only attractor is the completely disordered state, where all opinions coexist in the same proportion. For fixed lattice sizes, finite size effects cause a transition with the lenght of the relaxation period between coexistence and consensus. We made simulations for 2, 3, 4, 5 and 6 opinions in a square lattice and mean field calculations for an arbitrary number of opinions.

physics.soc-ph↗

arXiv2013

On the exit probability of the one dimensional q-voter model. Analytical results and simulations for large networks

We discuss the exit probability of the one dimensional $q$-voter model and present tools to obtain estimates about this probability both through simulations in large networks (around $10^7$ sites) and analyticaly in the limit where the network is infinetely large. We argue that the result $E(ρ) = \frac{ρ^q}{ρ^q + (1-ρ)^q}$, that was found in 3 previous works (2008 EPL 82 18006 and 2008 EPL 82 18007, for the case $q=2$ and 2011 PRE 84 031117, for $q>2$) using small networks (around $10^3$ sites), is a good approximation, but there are noticeable deviations for larger system sizes. We also show that, under some simple and intuitive hypothesis, the exit probability must obey the inequality, $\frac{ρ^q}{ρ^q + (1-ρ)} \leq E(ρ) \leq \fracρ{ρ+ (1-ρ)^q}$, in the infinite size limit. We believe this settles in the negative the suggestion made (2011 EPL 95 48005) that this result would be a finite size effect, with the exit probability actualy being a step function. We also show how the result, that the exit probability cannot be a step function, can be reconciled with the Galam unified frame, which was also a source of controversy.

physics.soc-ph↗

arXiv2012

Connections between the Sznajd Model with General Confidence Rules and graph theory

The Sznajd model is a sociophysics model, that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favour bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modelled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We present some graph theory concepts, together with examples, and comparisons between the mean-field and simulations in Barabási-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q>2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean-field, this would coincide with the q-voter model).

physics.soc-ph↗

arXiv2011

A Generalized Sznajd Model

In the last decade the Sznajd Model has been successfully employed in modeling some properties and scale features of both proportional and majority elections. We propose a new version of the Sznajd model with a generalized bounded confidence rule - a rule that limits the convincing capability of agents and that is essential to allow coexistence of opinions in the stationary state. With an appropriate choice of parameters it can be reduced to previous models. We solved this new model both in a mean-field approach (for an arbitrary number of opinions) and numerically in a Barabasi-Albert network (for three and four opinions), studying the transient and the possible stationary states. We built the phase portrait for the special cases of three and four opinions, defining the attractors and their basins of attraction. Through this analysis, we were able to understand and explain discrepancies between mean-field and simulation results obtained in previous works for the usual Sznajd Model with bounded confidence and three opinions. Both the dynamical system approach and our generalized bounded confidence rule are quite general and we think it can be useful to the understanding of other similar models.

cond-mat.stat-mech↗

arXiv2011

Coexistence of Interacting Opinions in a Generalized Sznajd Model

The Sznajd model is a sociophysics model that mimics the propagation of opinions in a closed society, where the interactions favour groups of agreeing people. It is based in the Ising and Potts ferromagnetic models and although the original model used only linear chains, it has since been adapted to general networks. This model has a very rich transient, that has been used to model several aspects of elections, but its stationary states are always consensus states. In order to model more complex behaviours we have, in a recent work, introduced the idea of biases and prejudices to the Sznajd model, by generalizing the bounded confidence rule that is common to many continuous opinion models. In that work we have found that the mean-field version of this model (corresponding to a complete network) allows for stationary states where non-interacting opinions survive, but never for the coexistence of interacting opinions. In the present work, we provide networks that allow for the coexistence of interacting opinions. Moreover, we show that the model does not become inactive, that is, the opinions keep changing, even in the stationary regime. We also provide results that give some insights on how this behaviour approaches the mean-field behaviour, as the networks are changed.

physics.soc-ph↗