arXiv subjects

Shlomi Reuveni

Publications and source records attributed to Shlomi Reuveni.

At least 55 records · Page 3Linked to original sources

arXiv2021

Resetting transition is governed by an interplay between thermal and potential energy

A dynamical process that takes a random time to complete, e.g., a chemical reaction, may either be accelerated or hindered due to resetting. Tuning system parameters such as temperature, viscosity or concentration, can invert the effect of resetting on the mean completion time of the process, which leads to a resetting transition. Though the resetting transition was recently studied for diffusion in a handful of model potentials, it is yet unknown whether the results follow any universality in terms of well-defined physical parameters. To bridge this gap, we propose a general framework which reveals that the resetting transition is governed by an interplay between thermal and potential energy. This result is illustrated for different classes of potentials that are used to model a wide variety of stochastic processes with numerous applications.

cond-mat.stat-mech↗

arXiv2021

Mean-performance of Sharp Restart II: Inequality Roadmap

Restarting a deterministic process always impedes its completion. However, it is known that restarting a random process can also lead to an opposite outcome -- expediting completion. Hence, the effect of restart is contingent on the underlying statistical heterogeneity of the process' completion times. To quantify this heterogeneity we bring a novel approach to restart: the methodology of inequality indices, which is widely applied in economics and in the social sciences to measure income and wealth disparity. Using this approach we establish an `inequality roadmap' for the mean-performance of sharp restart: a whole new set of universal inequality criteria that determine when restart with sharp timers (i.e. with fixed deterministic timers) decreases/increases mean completion. The criteria are based on a host of inequality indices including Bonferroni, Gini, Pietra, and other Lorenz-curve indices; each index captures a different angle of the restart-inequality interplay. Utilizing the fact that sharp restart can match the mean-performance of any general restart protocol, we prove -- with unprecedented precision and resolution -- the validity of the following statement: restart impedes/expedites mean completion when the underlying statistical heterogeneity is low/high.

cond-mat.stat-mech↗

arXiv2021

A Unified Approach to Gated Reactions on Networks

For two molecules to react they first have to meet. Yet, reaction times are rarely on par with the first-passage times that govern such molecular encounters. A prime reason for this discrepancy is stochastic transitions between reactive and non-reactive molecular states, which results in effective gating of product formation and altered reaction kinetics. To better understand this phenomenon we develop a unifying approach to gated reactions on networks. We first show that the mean and distribution of the gated reaction time can always be expressed in terms of ungated first-passage and return times. This relation between gated and ungated kinetics is then explored to reveal universal features of gated reactions. The latter are exemplified using a diverse set of case studies which are also used to expose the exotic kinetics that arises due to molecular gating.

cond-mat.stat-mech↗

arXiv2020

Diffusion with Local Resetting and Exclusion

Stochastic resetting models diverse phenomena across numerous scientific disciplines. Current understanding stems from the renewal framework, which relates systems subject to global resetting to their non-resetting counterparts. Yet, in interacting many-body systems, even the simplest scenarios involving resetting give rise to the notion of local resetting, whose analysis falls outside the scope of the renewal approach. A prime example is that of diffusing particles with excluded volume interactions that independently attempt to reset their position to the origin of a 1D lattice. With renewal rendered ineffective, we instead employ a mean-field approach whose validity is corroborated via extensive numerical simulations. The emerging picture sheds first light on the non-trivial interplay between interactions and resetting in many-body systems.

cond-mat.stat-mech↗

arXiv2020

Tail-behavior roadmap for sharp restart

Many tasks are accomplished via random processes. The completion time of such a task can be profoundly affected by restart: the occasional resetting of the task's underlying random process. Consequently, determining when restart will impede or expedite task completion is a subject of major importance. In recent years researchers explored this subject extensively, with main focus set on average behavior, i.e. on mean completion times. On the one hand, the mean approach asserts the centrality of "sharp restart" -- resetting with deterministic (fixed) timers. On the other hand, a significant drawback of the mean approach is that it provides no insight regarding tail behavior, i.e. the occurrence likelihood of extreme completion times. Addressing sharp restart, and shifting the focus from means to extremes, this paper establishes a comprehensive tail-behavior analysis of completion times. Employing the reliability-engineering notion of hazard rate, the analysis yields a set of universal results that determine -- from a tail-behavior perspective -- when sharp restart will impede or expedite task completion. The universal results are formulated in terms of explicit and highly applicable hazard-rate criteria. With the novel results at hand, a universal average-&-tail classification manual for sharp restart is devised. The manual specifies general scenarios in which -- rather counter-intuitively -- sharp restart has an opposite effect on average behavior and on tail behavior: decreasing mean completion times while dramatically increasing the likelihood of extreme completion times; and, conversely, increasing mean completion times while dramatically decreasing the likelihood of extreme completion times.

cond-mat.stat-mech↗

arXiv2020

Growth-laws and invariants from ribosome biogenesis in lower Eukarya

Eukarya and Bacteria are the most evolutionarily distant domains of life, which is reflected by differences in their cellular structure and physiology. For example, Eukarya feature membrane-bound organelles such as nuclei and mitochondria, whereas Bacteria have none. The greater complexity of Eukarya renders them difficult to study from both an experimental and theoretical perspective. However, encouraged by a recent experimental result showing that budding yeast (a unicellular eukaryote) obeys the same proportionality between ribosomal proteome fractions and cellular growth rates as Bacteria, we derive a set of relations describing eukaryotic growth from first principles of ribosome biogenesis. We recover the observed ribosomal protein proportionality, and then continue to obtain two growth-laws for the number of RNA polymerases synthesizing ribosomal RNA per ribosome in the cell. These growth-laws, in turn, reveal two invariants of eukaryotic growth, i.e. quantities predicted to be conserved by Eukarya regardless of growth conditions. The invariants, which are the first of their kind for Eukarya, clarify the coordination of transcription and translation kinetics as required by ribosome biogenesis, and link these kinetic parameters to cellular physiology. We demonstrate application of the relations to the yeast S. cerevisiae and find the predictions to be in good agreement with currently available data. We then outline methods to quantitatively deduce several unknown kinetic and physiological parameters. The analysis is not specific to S. cerevisiae and can be extended to other lower (unicellular) Eukarya when data become available. The relations may also have relevance to certain cancer cells which, like bacteria and yeast, exhibit rapid cell proliferation and ribosome biogenesis.

physics.bio-ph↗

arXiv2020

Thermodynamic uncertainty relation for systems with unidirectional transitions

We derive a thermodynamic uncertainty relation (TUR) for systems with unidirectional transitions. The uncertainty relation involves a mixture of thermodynamic and dynamic terms. Namely, the entropy production from bidirectional transitions, and the net flux of unidirectional transitions. The derivation does not assume a steady-state, and the results apply equally well to transient processes with arbitrary initial conditions. As every bidirectional transition can also be seen as a pair of separate unidirectional ones, our approach is equipped with an inherent degree of freedom. Thus, for any given system, an ensemble of valid TURs can be derived. However, we find that choosing a representation that best matches the systems dynamics over the observation time will yield a TUR with a tighter bound on fluctuations. More precisely, we show a bidirectional representation should be replaced by a unidirectional one when the entropy production associated with the transitions between two states is larger than the sum of the net fluxes between them. Thus, in addition to offering TURs for systems where such relations were previously unavailable, the results presented herein also provide a systematic method to improve TUR bounds via physically motivated replacement of bidirectional transitions with pairs of unidirectional transitions. The power of our approach and its implementation are demonstrated on a model for random walk with stochastic resetting and on the Michaelis-Menten model of enzymatic catalysis.

cond-mat.stat-mech↗

arXiv2020

Experimental realization of diffusion with stochastic resetting

Stochastic resetting is prevalent in natural and man-made systems giving rise to a long series of non-equilibrium phenomena. Diffusion with stochastic resetting serves as a paradigmatic model to study these phenomena, but the lack of a well-controlled platform by which this process can be studied experimentally has been a major impediment to research in the field. Here, we report the experimental realization of colloidal particle diffusion and resetting via holographic optical tweezers. We provide the first experimental corroboration of central theoretical results, and go on to measure the energetic cost of resetting in steady-state and first-passage scenarios. In both cases, we show that this cost cannot be made arbitrarily small due to fundamental constraints on realistic resetting protocols. The methods developed herein open the door to future experimental study of resetting phenomena beyond diffusion.

cond-mat.stat-mech↗

arXiv2020

Mean-performance of sharp restart I: Statistical roadmap

Restart is a general framework, of prime importance and wide applicability, for expediting first-passage times and completion times of general stochastic processes. Restart protocols can use either deterministic or stochastic timers. Restart protocols with deterministic timers -- "sharp restart" -- assume a principal role: if there exists a restart protocol that improves mean-performance, then there exists a sharp-restart protocol that performs as good or better. This paper, the first of a duo, presents a comprehensive mean-performance analysis of sharp restart. Using statistical methods, the analysis establishes universal criteria that determine when sharp restart improves or worsens mean-performance, i.e., decreases or increases mean first-passage/completion times. These criteria are akin to those recently discovered for the most widely applied restart protocols -- "exponential restart" -- which use exponentially-distributed timers. However, while the exponential-restart criteria cover only the case of slow timers, the sharp-restart criteria established here further cover the cases of fast, critical, and general timers; moreover, the latter criteria address the very existence of timers with which sharp restart improves or worsens mean-performance. Using the slow-timers criteria, we discover a general scenario for which: sharp restart improves mean-performance, whereas exponential restart worsens mean-performance. The potency of the novel results presented here is demonstrated by examples, and by the results' application to canonical diffusion processes.

cond-mat.stat-mech↗

arXiv2020

Search with home returns provides advantage under high uncertainty

Many search processes are conducted in the vicinity of a favored location, i.e., a home, which is visited repeatedly. Foraging animals return to their dens and nests to rest, scouts return to their bases to resupply, and drones return to their docking stations to recharge or refuel. Yet, despite its prevalence, very little is known about search with home returns as its analysis is much more challenging than that of unconstrained, free-range, search. Here, we develop a theoretical framework for search with home returns. This makes no assumptions on the underlying search process and is furthermore suited to treat generic return and home-stay strategies. We show that the solution to the home-return problem can then be given in terms of the solution to the corresponding free-range problem---which not only reduces overall complexity but also gives rise to a simple, and universal, phase-diagram for search. The latter reveals that search with home returns outperforms free-range search in conditions of high uncertainty. Thus, when living gets rough, a home will not only provide warmth and shelter but also allow one to locate food and other resources quickly and more efficiently than in its absence.

cond-mat.stat-mech↗

arXiv2020

Diffusion with resetting in a logarithmic potential

We study the effect of resetting on diffusion in a logarithmic potential. In this model, a particle diffusing in a potential $U(x) = U_0\log|x|$ is reset, i.e., taken back to its initial position, with a constant rate $r$. We show that this analytically tractable model system exhibits a series of phase transitions as a function of a single parameter, $βU_0$, the ratio of the strength of the potential to the thermal energy. For $βU_0<-1$ the potential is strongly repulsive, preventing the particle from reaching the origin. Resetting then generates a non-equilibrium steady state which is characterized exactly and thoroughly analyzed. In contrast, for $βU_0>-1$ the potential is either weakly repulsive or attractive and the diffusing particle eventually reaches the origin. In this case, we provide a closed form expression for the subsequent first-passage time distribution and show that a resetting transition occurs at $βU_0=5$. Namely, we find that resetting can expedite arrival to the origin when $-1<βU_0<5$, but not when $βU_0>5$. The results presented herein generalize results for simple diffusion with resetting -- a widely applicable model that is obtained from ours by setting $U_0=0$. Extending to general potential strengths, our work opens the door to theoretical and experimental investigation of a plethora of problems that bring together resetting and diffusion in logarithmic potential.

cond-mat.stat-mech↗

arXiv2019

Invariants of motion with stochastic resetting and space-time coupled returns

Motion under stochastic resetting serves to model a myriad of processes in physics and beyond, but in most cases studied to date resetting to the origin was assumed to take zero time or a time decoupled from the spatial position at the resetting moment. However, in our world, getting from one place to another always takes time and places that are further away take more time to be reached. We thus set off to extend the theory of stochastic resetting such that it would account for this inherent spatio-temporal coupling. We consider a particle that starts at the origin and follows a certain law of stochastic motion until it is interrupted at some random time. The particle then returns to the origin via a prescribed protocol. We study this model and surprisingly discover that the shape of the steady-state distribution which governs the stochastic motion phase does not depend on the return protocol. This shape invariance then gives rise to a simple, and generic, recipe for the computation of the full steady-state distribution. Several case studies are analyzed and a class of processes whose steady-state is completely invariant with respect to the speed of return is highlighted. For processes in this class we recover the same steady-state obtained for resetting with instantaneous returns---irrespective of whether the actual return speed is high or low. Our work significantly extends previous results on motion with stochastic resetting and is expected to find various applications in statistical, chemical, and biological physics.

cond-mat.stat-mech↗

arXiv2019

Gumbel Central Limit Theorem for Max-Min and Min-Max

The Max-Min and Min-Max of matrices arise prevalently in science and engineering. However, in many real-world situations the computation of the Max-Min and Min-Max is challenging as matrices are large and full information about their entries is lacking. Here we take a statistical-physics approach and establish limit-laws -- akin to the Central Limit Theorem -- for the Max-Min and Min-Max of large random matrices. The limit-laws intertwine random-matrix theory and extreme-value theory, couple the matrix-dimensions geometrically, and assert that Gumbel statistics emerge irrespective of the matrix-entries' distribution. Due to their generality and universality, as well as their practicality, these novel results are expected to have a host of applications in the physical sciences and beyond.

cond-mat.stat-mech↗

arXiv2019

Poisson-process limit-laws yield Gumbel Max-Min and Min-Max

"A chain is only as strong as its weakest link" says the proverb. But what about a collection of statistically identical chains: How long till all chains fail? The answer to this question is given by the Max-Min of a matrix whose $\left(i,j\right)$ entry is the failure time of link $j$ of chain $i$: take the minimum of each row, and then the maximum of the rows' minima. The corresponding Min-Max is obtained by taking the maximum of each column, and then the minimum of the columns' maxima. The Min-Max applies to the storage of critical data. Indeed, consider multiple backup copies of a set of critical data items, and consider the $\left(i,j\right)$ matrix entry to be the time at which item $j$ on copy $i$ is lost; then, the Min-Max is the time at which the first critical data item is lost. In this paper, we address random matrices whose entries are independent and identically distributed random variables. We establish Poisson-process limit-laws for the row's minima and for the columns' maxima. Then, we further establish Gumbel limit-laws for the Max-Min and for the Min-Max. The limit-laws hold whenever the entries' distribution has a density, and the Gumbel limit-laws yield highly applicable approximation tools and design tools for large random matrices.

cond-mat.stat-mech↗

arXiv2019

Diffusion with stochastic resetting is invariant to return speed

The canonical Evans--Majumdar model for diffusion with stochastic resetting to the origin assumes that resetting takes zero time: upon resetting the diffusing particle is teleported back to the origin to start its motion anew. However, in reality, getting from one place to another takes a finite amount of time which must be accounted for as diffusion with resetting already serves as a model for a myriad of processes in physics and beyond. Here we consider a situation where upon resetting the diffusing particle returns to the origin at a finite (rather than infinite) speed. This creates a coupling between the particle's random position at the moment of resetting and its return time, and further gives rise to a non-trivial cross-talk between two separate phases of motion: the diffusive phase and the return phase. We show that each of these phases relaxes to the stead-state in a unique manner; and while this could have also rendered the total relaxation dynamics extremely non-trivial our analysis surprisingly reveals otherwise. Indeed, the time-dependent distribution describing the particle's position in our model is completely invariant to the speed of return. Thus, whether returns are slow or fast, we always recover the result originally obtained for diffusion with instantaneous returns to the origin.

cond-mat.stat-mech↗

arXiv2019

Local time of diffusion with stochastic resetting

Diffusion with stochastic resetting has recently emerged as a powerful modeling tool with a myriad of potential applications. Here, we study local time in this model, covering situations of free and biased diffusion with, and without, the presence of an absorbing boundary. Given a Brownian trajectory that evolved for $t$ units of time, the local time is simply defined as the total time the trajectory spent in a small vicinity of its initial position. However, as Brownian trajectories are stochastic --- the local time itself is a random variable which fluctuates round and about its mean value. In the past, the statistics of these fluctuations has been quantified in detail; but not in the presence of resetting which biases the particle to spend more time near its starting point. Here, we extend past results to include the possibility of stochastic resetting with, and without, the presence of an absorbing boundary and/or drift. We obtain exact results for the moments and distribution of the local time and these reveal that its statistics usually admits a simple form in the long-time limit. And yet, while fluctuations in the absence of stochastic resetting are typically non-Gaussian --- resetting gives rise to Gaussian fluctuations. The analytical findings presented herein are in excellent agreement with numerical simulations.

cond-mat.stat-mech↗

arXiv2019

Péclet number governs transition to acceleratory restart in drift-diffusion

First-passage processes can be divided in two classes: those that are accelerated by the introduction of restart and those that display an opposite response. In physical systems, a transition between the two classes may occur as governing parameters are varied to cross a universal tipping point. However, a fully tractable model system to teach us how this transition unfolds is still lacking. To bridge this gap, we quantify the effect of stochastic restart on the first-passage time of a drift-diffusion process to an absorbing boundary. There, we find that the transition is governed by the Péclet number ($Pe$) --- the ratio between the rates of advective and diffusive transport. When $Pe>1$ the process is drift-controlled and restart can only hinder its completion. In contrast, when $0\leq~Pe<1$ the process is diffusion-controlled and restart can speed-up its completion by a factor of $\sim1/Pe$. Such speedup occurs when the process is restarted at an optimal rate $r^{\star}\simeq r_0^{\star}\left(1-Pe\right)$, where $r_0^{\star}$ stands for the optimal restart rate in the pure-diffusion limit. The transition considered herein stands at the core of restart phenomena and is relevant to a large variety of processes that are driven to completion in the presence of noise. Each of these processes has unique characteristics, but our analysis reveals that the restart transition resembles other phase transitions --- some of its central features are completely generic.

cond-mat.stat-mech↗

arXiv2019

Occupancy correlations in the asymmetric simple inclusion process

The asymmetric simple inclusion process (ASIP) --- a lattice-gas model for unidirectional transport with irreversible aggregation --- has been proposed as an inclusion counterpart of the asymmetric simple exclusion process and as a batch service counterpart of the tandem Jackson network. To date, analytical tractability of the model has been limited: while the average particle density in the model is easy to compute, very little is known about its joint occupancy distribution. To partially bridge this gap, we study occupancy correlations in the ASIP. We take an analytical approach to this problem and derive an exact formula for the covariance matrix of the steady-state occupancy vector. We verify the validity of this formula numerically in small ASIP systems, where Monte-Carlo simulations can provide reliable estimates for correlations in reasonable time, and further use it to draw a comprehensive picture of spatial occupancy correlations in ASIP systems of arbitrary size.

cond-mat.stat-mech↗