arXiv subjects

Luca Peliti

Publications and source records attributed to Luca Peliti.

At least 19 recordsLinked to original sources

arXiv2025

Path-integrals and optimal paths for the fractional Ornstein-Uhlenbeck process

We derive the path-integral representation of the fractional Ornstein-Uhlenbeck process driven by Riemann-Liouville fractional Gaussian noise, for both the subdiffusive and superdiffusive regimes. We express the corresponding action, which is a quadratic functional of individual trajectories of the process, in two alternative but equivalent forms: either as a fractional integral or as a double integral with a nonlocal kernel. Moreover, we determine in closed form the optimal (action-minimizing) paths conditioned to reach a prescribed point at a fixed time moment and discuss their behavior, which appears to be non-intuitive for subdiffusive processes in the presence of a strong confining potential.

cond-mat.stat-mech↗

arXiv2025

One-dimensional lattice random walks in a Gaussian random potential

We study random walks evolving in continuous time on a one-dimensional lattice where each site $x$ hosts a quenched random potential $U_x$. The potentials on different sites are independent, identically distributed Gaussian random variables. We analyze three distinct models that specify how the transition rates depend on $U_x$: the random-force-like model, random walks with randomized stepping times, and the Gaussian trap model. Our analysis focuses on five key disorder-dependent quantities defined for a finite chain with $N$ sites: the probability current, its reciprocal (the resistance), the splitting probability $E_-$, the mean first-passage time $T_N$, and the diffusion coefficient $D_N$ in a periodic chain. By determining the moments of these random variables, we demonstrate that the probability current and resistance are not self-averaging, which leads to pronounced differences between their average and typical behaviors. In contrast, $E_-$, $T_N$ and $D_N$ become self-averaging when $N \to \infty$, though they exhibit strong sample-to-sample fluctuations for finite $N$.

cond-mat.stat-mech↗

arXiv2025

Excess dissipation shapes symmetry breaking in non-equilibrium currents

Most natural thermodynamic systems operate far from equilibrium, developing persistent currents and organizing into non-equilibrium stationary states (NESSs). Yet, the principles by which such systems self-organize, breaking equilibrium symmetries under external and internal constraints, remain unclear. Here, we establish a general connection between symmetry breaking and dissipation in mesoscopic stochastic systems described by Langevin dynamics. Using a geometric framework based on the inverse diffusion matrix, we decompose the velocity field into excess (gradient) and housekeeping (residual) components. This provides a natural entropy production split: the excess part captures internal reorganization under non-equilibrium conditions, while the housekeeping part quantifies detailed-balance violation due to external forces. We derive an exact equality linking the two, along with an inequality identifying accessible thermodynamics. A weak-noise expansion of the stationary solution reveals the general geometry of the NESS velocity field, enabling a unified classification of steady states. We apply this framework to systems ranging from molecular machines to coupled oscillators, showing how symmetry breaking in trajectory space constrains NESS organization. We further extend our approach to systems with multiplicative noise, deriving how additional symmetry breaking relates to curved (space-dependent) metrics. Finally, we show that both the NESS velocity field and stationary distribution can be derived through variational functionals based on excess dissipation. This work sheds light on the intimate connection between geometric features, dissipative properties, and symmetry breaking, uncovering a classification of NESSs that reflects how emergent organization reflects physical non-equilibrium conditions.

cond-mat.stat-mech↗

arXiv2025

Content-Addressable Memory with a Content-Free Energy Function

Content-addressable memory, i.e. stored information that can be retrieved from content-based cues, is key to computation. Besides natural and artificial neural networks, physical learning systems have recently been shown to have remarkable ability in this domain. While classical neural network models encode memories as energy minima, biochemical systems have been shown to be able to process information based on purely kinetic principles. This opens the question of whether neural networks can also encode information kinetically. Here, we propose a minimal model for content-addressable memory in which the kinetics, and not the energy function, are used to encode patterns. We find that the performance of this kinetic encoding approach is comparable to that of classical energy-based encoding schemes. This highlights the fundamental significance of the kinetic stability of kinetic traps as an alternative to the thermodynamic stability of energy minima, offering new insights into the principles of computation in physical and synthetic systems.

cond-mat.stat-mech↗

arXiv2025

A simple model of a sequence-reading diffusion: non-self-averaging and self-averaging properties

Motivated by a question about the sensitivity of knots' diffusive motion to the actual sequence of nucleotides placed on a given DNA, here we study a simple model of a sequence-reading diffusion on a stretched chain with a frozen sequence of "letters" $A$ and $B$, having different interaction energies. The chain contains a single distortion - a hernia - which brings the two letters at its bottom together such that they interact. Due to interactions with the solvent, the hernia performs a random hopping motion along the chain with the transition rates dependent on its actual position. Our two focal questions are a) the dependence of various transport properties on the letters' interaction energy and b) whether these properties are self-averaging with respect to different realizations of sequences. We show that the current through a finite interval, the resistance of this interval and the splitting probabilities on this interval lack self-averaging. On the contrary, the mean first-passage time through a finite interval with $N$ sites and the diffusion coefficient in a periodic chain are self-averaging in the limit $N \to \infty$. Concurrently, two latter properties exhibit sample-to-sample fluctuations for finite $N$, as evidenced by numerical simulations.

cond-mat.stat-mech↗

arXiv2024

Adaptive efficiency of information processing in immune-pathogen co-evolution

Organisms have evolved immune systems that can counter pathogenic threats. The adaptive immune system in vertebrates consists of a diverse repertoire of immune receptors that can dynamically reorganize to specifically target the ever-changing pathogenic landscape. Pathogens in return evolve to escape the immune challenge, forming an co-evolutionary arms race. We introduce a formalism to characterize out-of-equilibrium interactions in co-evolutionary processes. We show that the rates of information exchange and entropy production can distinguish the leader from the follower in an evolutionary arms races. Lastly, we introduce co-evolutionary efficiency as a metric to quantify each population's ability to exploit information in response to the other. Our formalism provides insights into the conditions necessary for stable co-evolution and establishes bounds on the limits of information exchange and adaptation in co-evolving systems.

q-bio.PE↗

arXiv2023

Emergent cooperative behavior in transient compartments

We introduce a minimal model of multilevel selection on structured populations, considering the interplay between game theory and population dynamics. Through a bottleneck process, finite groups are formed with cooperators and defectors sampled from an infinite pool. After the fragmentation, these transient compartments grow until the carrying capacity is attained. Eventually, all compartments are merged, well mixed and the whole process is repeated. We show that cooperators, even if interacting only through mean-field intra-group interactions that favor defectors, may perform well because of the inter-group competition and the size diversity among the compartments. These cycles of isolation and coalescence may therefore be important in maintaining diversity among different species or strategies and may help to understand the underlying mechanisms of the scaffolding processes in the transition to multicellularity.

q-bio.PE↗

arXiv2023

Cell lineage statistics with incomplete population trees

Cell lineage statistics is a powerful tool for inferring cellular parameters, such as division rate, death rate or the population growth rate. Yet, in practice such an analysis suffers from a basic problem: how should we treat incomplete lineages that do not survive until the end of the experiment? Here, we develop a model-independent theoretical framework to address this issue. We show how to quantify fitness landscape, survivor bias and selection for arbitrary cell traits from cell lineage statistics in the presence of death, and we test this method using an experimental data set in which a cell population is exposed to a drug that kills a large fraction of the population. This analysis reveals that failing to properly account for dead lineages can lead to misleading fitness estimations. For simple trait dynamics, we prove and illustrate numerically that the fitness landscape and the survivor bias can in addition be used for the non-parametric estimation of the division and death rates, using only lineage histories. Our framework provides universal bounds on the population growth rate, and a fluctuation-response relation which quantifies the reduction of population growth rate due to the variability in death rate. Further, in the context of cell size control, we obtain generalizations of Powell's relation that link the distributions of generation times with the population growth rate, and show that the survivor bias can sometimes conceal the adder property, namely the constant increment of volume between birth and division.

q-bio.PE↗

arXiv2023

Classical uncertainty relations and entropy production in non-equilibrium statistical mechanics

We analyze F\"urth's 1933 classical uncertainty relations in the modern language of stochastic differential equations. Our interest is motivated by applications to non-equilibrium classical statistical mechanics. We show that F\"urth's uncertainty relations are a property enjoyed by martingales under the measure of a diffusion process. This result implies a lower bound on fluctuations in current velocities of entropic quantifiers of transitions in stochastic thermodynamics. In cases of particular interest, we recover an inequality well known in optimal mass transport relating the mean kinetic energy of the current velocity and the squared quadratic Wasserstein distance between the probability distributions of the entropy. In performing our analysis, we also avail us of an unpublished argument due to Krzysztof Gaw\c{e}dzki to derive a lower bound to the entropy production by transition described by Langevin-Kramers process in terms of the squared quadratic Wasserstein distance between the initial and final states of the transition. Finally, we illustrate how F\"urth's relations admit a straightforward extension to piecewise deterministic processes. We thus show that the results in the paper concern properties enjoyed by general Markov processes.

cond-mat.stat-mech↗

arXiv2022

Fluctuations of Heat in Driven Two-State Systems: Application to Single-Electron Box with Superconducting Gap

We use trajectory averaging to show that the energy dissipated in the nonequilibrium energy-state transitions of a driven two-state system satisfies a fluctuation-dissipation relation. This connection between the average energy dissipation induced by external driving and its fluctuations about equilibrium is preserved by an adiabatic approximation scheme. We use this scheme to obtain the heat statistics of a single-electron box with superconducting leads in the slow-driving regime, where the dissipated heat becomes normally distributed with a relatively high probability to be extracted from the environment rather than dissipated. We also discuss heat fluctuation relations for driven two-state transitions.

cond-mat.mes-hall↗

arXiv2022

Adaptive strategy in Kelly's horse races model

We formulate an adaptive version of Kelly's horse model in which the gambler learns from past race results using Bayesian inference. A known asymptotic scaling for the difference between the growth rate of the gambler and the optimal growth rate, known as the gambler'sregret, is recovered. We show how this adaptive strategy is related to the universal portfolio strategy, and we build improved adaptive strategies in which the gambler exploits information contained in the bookmaker odds distribution to reduce his/her initial loss of the capital during the learning phase.

cond-mat.stat-mech↗

arXiv2022

Frequency-frequency correlations of single-trajectory spectral densities of Gaussian processes

We investigate the stochastic behavior of the single-trajectory spectral density $S(ω,\mathcal{T})$ of several Gaussian stochastic processes, i.e., Brownian motion, the Ornstein-Uhlenbeck process, the Brownian gyrator model and fractional Brownian motion, as a function of the frequency $ω$ and the observation time $\mathcal{T}$. We evaluate in particular the variance and the frequency-frequency correlation of $S(ω,\mathcal{T})$ for different values of $ω$. We show that these properties exhibit different behaviors for different physical cases and can therefore be used as a sensitive probe discriminating between different kinds of random motion. These results may prove quite useful in the analysis of experimental data.

cond-mat.stat-mech↗

arXiv2022

Noise-to-signal ratio of single-trajectory spectral densities in centered Gaussian processes

We discuss the statistical properties of a single-trajectory power spectral density $S(ω,\mathcal{T})$ of an arbitrary real-valued centered Gaussian process $X(t)$, where $ω$ is the angular frequency and $\mathcal{T}$ the observation time. We derive a double-sided inequality for its noise-to-signal ratio and obtain the full probability density function of $S(ω,\mathcal{T})$. Our findings imply that the fluctuations of $S(ω,\mathcal{T})$ exceed its average value $μ(ω,\mathcal{T})$. This implies that using $μ(ω,\mathcal{T})$ to describe the behavior of these processes can be problematic. We finally evaluate the typical behavior of $S(ω,\mathcal{T})$ and find that it deviates markedly from the average $μ(ω,\mathcal{T})$ in most cases.

cond-mat.stat-mech↗

arXiv2021

Risk-utility tradeoff shapes memory strategies for evolving patterns

Keeping a memory of evolving stimuli is ubiquitous in biology, an example of which is immune memory for evolving pathogens. However, learning and memory storage for dynamic patterns still pose challenges in machine learning. Here, we introduce an analytical energy-based framework to address this problem. By accounting for the tradeoff between utility in keeping a high-affinity memory and the risk in forgetting some of the diverse stimuli, we show that a moderate tolerance for risk enables a repertoire to robustly classify evolving patterns, without much fine-tuning. Our approach offers a general guideline for learning and memory storage in systems interacting with diverse and evolving stimuli.

physics.bio-ph↗

arXiv2021

Learning and organization of memory for evolving patterns

Storing memory for molecular recognition is an efficient strategy for responding to external stimuli. Biological processes use different strategies to store memory. In the olfactory cortex, synaptic connections form when stimulated by an odor, and establish distributed memory that can be retrieved upon re-exposure. In contrast, the immune system encodes specialized memory by diverse receptors that recognize a multitude of evolving pathogens. Despite the mechanistic differences between the olfactory and the immune memory, these systems can still be viewed as different information encoding strategies. Here, we present a theoretical framework with artificial neural networks to characterize optimal memory strategies for both static and dynamic (evolving) patterns. Our approach is a generalization of the energy-based Hopfield model in which memory is stored as a network's energy minima. We find that while classical Hopfield networks with distributed memory can efficiently encode a memory of static patterns, they are inadequate against evolving patterns. To follow an evolving pattern, we show that a distributed network should use a higher learning rate, which in turn, can distort the energy landscape associated with the stored memory attractors. Specifically, narrow connecting paths emerge between memory attractors, leading to misclassification of evolving patterns. We demonstrate that compartmentalized networks with specialized subnetworks are the optimal solutions to memory storage for evolving patterns. We postulate that evolution of pathogens may be the reason for the immune system to encoded a focused memory, in contrast to the distributed memory used in the olfactory cortex that interacts with mixtures of static odors.

physics.bio-ph↗

arXiv2020

R. Fürth's 1933 paper "On certain relations between classical Statistics and Quantum Mechanics" ["Über einige Beziehungen zwischen klassischer Statistik und Quantenmechanik", \textit{Zeitschrift für Physik,} \textbf{81} 143-162]

We present a translation of the 1933 paper by R. Fürth in which a profound analogy between quantum fluctuations and Brownian motion is pointed out. This paper opened in some sense the way to the stochastic methods of quantization developed almost 30 years later by Edward Nelson and others.

physics.hist-ph↗

arXiv2019

The generality of transient compartmentalization and its associated error thresholds

Can prelife proceed without cell division? A recently proposed mechanism suggests that transient compartmentalization could have preceded cell division in prebiotic scenarios. Here, we study transient compartmentalization dynamics in the presence of mutations and noise in replication, as both can be detrimental the survival of compartments. Our study comprises situations where compartments contain uncoupled autocatalytic reactions feeding on a common resource, and systems based on RNA molecules copied by replicases, following a recent experimental study. Using the theory of branching processes, we show analytically that two regimes are possible. In the diffusion-limited regime, replication is asynchronous which leads to a large variability in the composition of compartments. In contrast, in a replication-limited regime, the growth is synchronous and thus the compositional variability is low. Typically, simple autocatalysts are in the former regime, while polymeric replicators can access the latter. For deterministic growth dynamics, we introduce mutations that turn functional replicators into parasites. We derive the phase boundary separating coexistence or parasite dominance as a function of relative growth, inoculation size and mutation rate. We show that transient compartmentalization allows coexistence beyond the classical error threshold, above which the parasite dominates. Our findings invite to revisit major prebiotic transitions, notably the transitions towards cooperation, complex polymers and cell division.

q-bio.PE↗

arXiv2019

Evolution and Probability

Life forms exhibit such a degree of exquisite organization that it seems impossible that they could have developed out of a process of trial and error, as intimated by the theory of Darwinian evolution. In this general public paper I discuss how differential reproduction rates work in producing an exceedingly high degree of improbability, and the conceptual tools of the theory of evolution help us to predict, to some degree, the course of evolution -- as it is routinely done, e.g., in the process leading to the yearly influenza vaccines.

q-bio.PE↗