We derive an Itô stochastic differential equation for entropy production in nonequilibrium Langevin processes. Introducing a random-time transformation, entropy production obeys a onedimensional drift-diffusion equation, independent of the underlying physical model. This transformation allows us to identify generic properties of entropy production. It also leads to an exact uncertainty equality relating the Fano factor of entropy production and the Fano factor of the random time, which we also generalize to non steady-state conditions. The laws of thermodynamics can be extended to mesoscopic systems [1][2][3][4][5]. For such systems, energy changes on the order of the thermal energy k B T are relevant. Here, k B is the Boltzmann constant and T the temperature. Therefore, thermodynamic observables associated with mesoscopic degrees of freedom are stochastic. A key example of such thermodynamics observables is the stochastic entropy production in nonequilibrium processes. Recent experimental advances in micromanipulation techniques permit the measurement of stochastic entropy production in the laboratory [6][7][8][9][10].Certain statistical properties of stochastic entropy production are generic, i.e., they are independent of the physical details of a system. Examples of such generic properties are the celebrated fluctuation theorems, for reviews see [2,4,5]. Recently, it was shown that infima and passage probabilities of entropy production are also generic [11]. Other statistical properties of entropy production are system-dependent, such as the mean value [12][13][14][15], the variance [16,17], the first-passage times of entropy production [18][19][20] and the large deviation function [21,22]. Nevertheless, these properties are sometimes constrained by universal bounds [11,14,16,17,[23][24][25][26][27]. It remains unclear which statistical properties of stochastic entropy production are generic, and why.In this Letter, we introduce a theoretical framework which addresses this question for nonequilibrium Langevin processes. We identify generic properties of entropy production by their independence of a stochastic variable τ which we call entropic time. We find that the evolution of steady-state entropy production as a function of τ is governed by a simple one-dimensional driftdiffusion process, independent of the underlying model. This allows us to identify a set of generic properties of entropy production and obtain exact results characterizing entropy production fluctuations.We consider a mesoscopic system described by n slow degrees of freedom X = (X 1 (t), X 2 (t), . . . , X n (t)) T . The system is in contact with a thermostat at temperature T . The stochastic dynamics of the system can be described by the probability distribution P ( X, t) to find the system in a configuration X at time t . This probability distribution satisfies the Smoluchowski equationwhere the probability current is given byHere we have introduced the force at time t, F = − ∇U ( X(t), t) + f ( X(t), t), where U is a potential and f is a...

We study stochastic copying schemes in which discrimination between a right and a wrong match is achieved via different kinetic barriers or different binding energies of the two matches. We demonstrate that, in single-step reactions, the two discrimination mechanisms are strictly alternative and can not be mixed to further reduce the error fraction. Close to the lowest error limit, kinetic discrimination results in a diverging copying velocity and dissipation per copied bit. On the opposite, energetic discrimination reaches its lowest error limit in an adiabatic regime where dissipation and velocity vanish. By analyzing experimentally measured kinetic rates of two DNA polymerases, T7 and Polγ, we argue that one of them operates in the kinetic and the other in the energetic regime. Finally, we show how the two mechanisms can be combined in copying schemes implementing error correction through a proofreading pathway.PACS numbers: 87.10. Vg, 87.18.Tt, 05.70.Ln Living organisms need to process signals in a fast and reliable way. Copying information is a task of particular relevance, as it is required for the replication of the genetic code, the transcription of DNA into mRNA, and its translation into a protein. Reliability is fundamental, since errors can result in the costly (or harmful) production of a non-functional protein. Indeed, cells have developed mechanisms to reduce the copying error rate η to values as low as η ∼ 10 −4 for protein transcription-translation [1] and η ∼ 10 −10 for DNA replication [2]. Such mechanisms include multiple discrimination steps [1, 2] and pathways to undo wrong copies as in proofreading [2,[4][5][6] or backtracking [7].Biological information is copied by thermodynamic machines that operate at a finite temperature. There is agreement that this fact alone implies a lower limit on the error rate. However, contrasting results have been obtained regarding the nature of this limit. In particular, it is not clear when it is reached in a slow and quasi-adiabiatic regime, or in a fast and dissipative one. As clarified by Bennett [8], information can be copied adiabatically. Indeed, the copying scheme proposed in Hopfield's seminal proofreading paper [2] reaches its minimum error at zero velocity and zero dissipation [9]. In contrast, a copolymerization model proposed few years later by Bennett [1,11,12], achieves its minimum error in a highly dissipative regime, where velocity and dissipation diverge. Some of the biological literature has favoured that the minimum error is achieved in near-equilibrium conditions [9]. This view is however not unanimous [13]. Recent biophysical literature supports a dissipative minimum error limit [11,12,14,15]. Similar disagreements are also present in models including proofreading. The proofreading model in [1] dissipates systematically less than the corresponding copying, while in other models [2, 4], at low errors, dissipation comes mainly from the proofreading step.In this Letter, we show how these contrasting results can be rationalized noting that...

The assembly of an ecosystem such as a tropical forest depends crucially on the species interaction network, and the deduction of its rules is a formidably complex problem. In spite of this, many recent studies using Hubbell's neutral theory of biodiversity and biogeography have demonstrated that the resulting emergent macroscopic behaviour of the ecosystem at or near a stationary state shows a surprising simplicity reminiscent of many physical systems. Indeed the symmetry postulate, that the effective birth and death rates are species-independent within a single trophic level, allows one to make analytical predictions for various static distributions such as the relative species abundance, beta-diversity and the species-area relationship. In contrast, there have only been a few studies of the dynamics and stability of tropical rain forests. Here we consider the dynamical behaviour of a community, and benchmark it against the exact predictions of a neutral model near or at stationarity. In addition to providing a description of the relative species abundance, our analysis leads to a quantitative understanding of the species turnover distribution and extinction times, and a measure of the temporal scales of neutral evolution. Our model gives a very good description of the large quantity of data collected in Barro Colorado Island in Panama in the period 1990-2000 with just three ecologically relevant parameters and predicts the dynamics of extinction of the existing species.

We study the properties of general Lotka-Volterra models with competitive interactions. The intensity of the competition depends on the position of species in an abstract niche space through an interaction kernel. We show analytically and numerically that the properties of these models change dramatically when the Fourier transform of this kernel is not positive definite, due to a pattern forming instability. We estimate properties of the species distributions, such as the steady number of species and their spacings, for different types of interactions, including stretched exponential and constant kernels.PACS numbers: 87.23. Cc, 45.70.Qj, It is widely believed that competition among species greatly influences global features of ecosystems. One of the most relevant is the fact that ecosystems can host a limited number of species. The common explanation is the so-called limiting similarity [1] and involves representing species as points in an abstract niche space, whose coordinates quantify the phenotypic traits of a species which are relevant for the consumption of resources, like the typical size of individuals, but also preferred prey, optimal temperature and so on. On general grounds, one expects that a species experiences a stronger competition with the closer species in this space. As a consequence, a species can survive if it is able to maintain its distance with the others above a minimum value which depends on the competition strength. On the contrary, a species will outcompete another when the distance between them becomes too small, due to the unavoidable difference in how efficiently they feed on the resources. This is the phenomenon of competitive exclusion [2], which is a basis of the concept of ecological niche. Thus, one expects a stable ecosystem to display a finite number of species, approximately equidistant in niche space. The finiteness of the number of species has been observed in several competition models [3] and rigorously demonstrated for a general class of them [4].Deviations from the above scenario have aroused renewed interest recently, when it was observed numerically [5] that the equilibrium state of rather standard models is not always characterized by a homogeneous distribution of species in niche space. Instead, clumpy distributions, with clusters of many species separated by unoccupied regions, are observed. Evidences of a similar phenomenon have been observed recently in evolutionary models [6], suggesting that a theoretical explanation of these patterns could bring new insights in the study of speciation mechanisms [7].In this Letter, we study the Lotka-Volterra (LV) competitive model as the prototype of competitive systems (i.e. population models in which the growth of a species negatively affects the growth rate of others). The statistical properties of many-species LV models have been studied using particular symmetries of the interaction matrix [8], but not much is known on the statistics of a competitive case. We stress that the competitive LV system appears in contexts a...