Dynamic phase transitions in simple driven kinetic networks

Abstract

We analyze the probability distribution for entropy production rates of trajectories evolving on a class of out-of-equilibrium kinetic networks. These networks can serve as simple models for driven dynamical systems, where energy fluxes typically result in non-equilibrium dynamics. By analyzing the fluctuations in the entropy production, we demonstrate the emergence, in a large system size limit, of a dynamic phase transition between two distinct dynamical regimes.The study of fluctuation phenomena is one of the central endeavors of non-equilibrium statistical mechanics. Analysis of fluctuations in non-equilibrium processes have, for example, led to the discovery of the fluctuation theorems, which have helped elucidate how macroscopic notions of irreversibility emerge from microscopic laws [1][2][3]. More recently, theoretical and numerical analysis of the statistics of rare fluctuations in driven lattice gas models [4,5], exclusion processes [6], zero-range processes [7], 1D models of transport [8], and models of glass formers [9,10] have revealed the presence of coexisting ensembles of trajectories and so-called dynamic phase transitions between them [4,5,8,11]. In this paper, we analyze the statistics of rare fluctuations in entropy production rates for certain model non-equilibrium, or driven, kinetic networks (see Fig. 1). While this Markovian system, with effectively one-particle dynamics, lacks much of the complexity of previously studied driven systems [4-8], we show -numerically and analyticallythe presence of two dynamical phases, each with a characteristic entropy production rate. This demonstration shows that singularities in trajectory space can in fact arise even in very simple driven kinetic networks with a single degree of freedom. Driven kinetic networks of this general flavor are used to model a variety of physical, chemical, and biological systems including molecular motor dynamics [12,13]; cellular feedback, control, and regulation [14]; and kinetic proofreading mechanisms [15,16]. Physically, the dynamic phase transition serves to enhance the probability of observing large fluctuations in the dynamical behavior of these hopping processes.We study dynamical fluctuations of a system evolving on cyclical or periodic driven kinetic networks with some heterogeneity in the transition rates. We consider two types of cyclic networks, which we hereafter refer to as the ring network and the triangle network. The ring network connects N states in a circle with transition rates x in the clockwise direction and 1 in the reverse direction. The network has translational symmetry, but we also construct a variation of the ring network with that symmetry broken by a link we call the heterogeneous link, or h-link. As shown in Fig.

Heat dissipation guides activation in signaling proteins

“…2 suggests that the first slope maximum in ATP-bound Src's rate curve (related to the first peak of χ ω ) corresponds to the transition between the near-equilibrium and dissipative regimes; the second, less dramatic maximum seems to be related to a transition between the two prominent peaks within the dissipative regime. In comparison with fully nonequilibrium systems, these crossovers are reminiscent of "dynamical phase transitions" that have been observed between different regimes of dissipation in simple, driven networks (10,11,32). The response function peaks we observe here only occur within transient relaxation dynamics, and thus do not represent true phase transitions in the thermodynamic limit.…”

Thermodynamics of Statistical Inference by Cells

“…In particular, it will be interesting to see if these results change for receptors modeled by heterogeneous Markov networks that are not strictly ringlike in nature. Recent work indicates that at large entropy production the dynamics of such networks may be independent of details of the underlying topology, suggesting that our basic picture should hold even for more complicated nonequilibrium receptors [35]. An additional extension to our model would be to consider externally varying concentrations by implementing a sensory adaptive system (SAS) as was done in recent papers [36,37].…”

Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables

“…An important observation is that the bounds on fluctuations of a counting observable and its FPTs are controlled by the average dynamical activity, in analogy to the role played by the entropy production in the case of currents [1,13]. We hope these results will add to the growing body of work applying large deviation ideas and methods to the study of dynamics in driven systems [29][30][31][32][33][34][35][36][37][38][39][40][41], glasses [25,[42][43][44][45][46][47], protein folding and signaling networks [48][49][50][51], open quantum systems [52][53][54][55][56][57][58][59][60][61][62][63][64], and many other problems in nonequilibrium [65][66][67][68][69][70][71][72].…”