SciPost Phys. 15, 164 (2023) ·
published 16 October 2023
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The characterization of density correlations in the presence of strongly fluctuating interfaces has always been considered a difficult problem in statistical mechanics. Here we study - by using recently developed exact field-theoretical techniques - density correlations for an interface with endpoints on a wall forming a droplet in 2D. Our framework applies to interfaces entropically repelled by a hard wall as well as to wetting transitions. In the former case bubbles adsorbed on the interface are taken into account by the theory which yields a systematic treatment of finite-size corrections to one- and two-point functions and show how these are related to Brownian excursions. Our analytical predictions are confirmed by Monte Carlo simulations without free parameters. We also determine one- and two-point functions at wetting by using integrable boundary field theory. We show that correlations are long ranged for entropic repulsion and at wetting. For both regimes we investigate correlations in momentum space by generalizing the notion of interface structure factor to semi-confined systems. Distinctive signatures of the two regimes manifest in the structure factor through a term that we identify on top of the capillary-wave one.
SciPost Phys. 9, 030 (2020) ·
published 2 September 2020
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We derive an expression for the minimal rate of entropy that sustains two reservoirs at different temperatures $T_0$ and $T_\ell$. The law displays an intuitive $\ell^{-1}$ dependency on the relative distance and a characterisic $\log^2 (T_\ell/T_0)$ dependency on the boundary temperatures. First we give a back-of-envelope argument based on the Fourier Law (FL) of conduction, showing that the least-dissipation profile is exponential. Then we revisit a model of a chain of oscillators, each coupled to a heat reservoir. In the limit of large damping we reobtain the exponential and squared-log behaviors, providing a self-consistent derivation of the FL. For small damping "equipartition frustration" leads to a well-known balistic behaviour, whose incompatibility with the FL posed a long-time challenge.
SciPost Phys. Lect. Notes 76 (2023) ·
published 30 October 2023
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In statistical mechanics, the generally called Stirling approximation is actually an approximation of Stirling's formula. In this article, it is shown that the term that is dropped is in fact the one that takes fluctuations into account. The use of the Stirling's exact formula forces us to reintroduce them into the already proposed solutions of well-know puzzles such as the extensivity paradox or the Gibbs' paradox of joining two volumes of identical gas. This amendment clearly results in a gain in consistency and rigor of these solutions.
SciPost Phys. 13, 076 (2022) ·
published 30 September 2022
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We propose an information-theoretical measure, the \textit{relative cluster entropy} $\mathcal{D_{C}}[P \| Q] $, to discriminate among cluster partitions characterised by probability distribution functions $P$ and $Q$. The measure is illustrated with the clusters generated by pairs of fractional Brownian motions with Hurst exponents $H_1$ and $H_2$ respectively. For subdiffusive, normal and superdiffusive sequences, the relative entropy sensibly depends on the difference between $H_1$ and $H_2$. By using the \textit{minimum relative entropy} principle, cluster sequences characterized by different correlation degrees are distinguished and the optimal Hurst exponent is selected. As a case study, real-world cluster partitions of market price series are compared to those obtained from fully uncorrelated sequences (simple Browniam motions) assumed as a model. The \textit{minimum relative cluster entropy} yields optimal Hurst exponents $H_1=0.55$, $H_1=0.57$, and $H_1=0.63$ respectively for the prices of DJIA, S\&P500, NASDAQ: a clear indication of non-markovianity. Finally, we derive the analytical expression of the relative cluster entropy and the outcomes are discussed for arbitrary pairs of power-laws probability distribution functions of continuous random variables.
Marcelo Tozo Araujo, Jorge Chahine, Elso Drigo Filho, Regina Maria Ricotta
SciPost Phys. Proc. 14, 015 (2023) ·
published 23 November 2023
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Recently, a mathematical method to solve the Fokker Plank equation (FPE) enabled the analysis of the protein folding kinetics, through the construction of the temporal evolution of the probability density. A symmetric tri-stable potential function was used to describe the unfolded and folded states of the protein as well as an intermediate state of the protein. In this paper, the main points of the methodology are reviewed, based on the algebraic Supersymmetric Quantum Mechanics (SQM) formalism, and new results on the kinetics of the evolution of the system characterized in terms of the diffusion parameter are presented.
