In the search for the low-complexity sequences in prokaryotic and eukaryotic genomes: how to derive a coherent picture from global and local entropy measures

We investigate on a possible way to connect the presence of Low-Complexity Sequences (LCS) in DNA genomes and the nonstationary properties of base correlations. Under the hypothesis that these variations signal a change in the DNA function, we use a new technique, called Non-Stationarity Entropic Index (NSEI) method, and we prove that this technique is an efficient way to detect functional changes with respect to a random baseline. The remarkable aspect is that NSEI does not imply any training data or fitting parameter, the only arbitrarity being the choice of a marker in the sequence. We make this choice on the basis of biological information about LCS distributions in genomes. We show that there exists a correlation between changing the amount in LCS and the ratio of long- to short-range correlation

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

Peer reviewedPublisher PD

Fluctuation theorems for non-Markovian quantum processes

Exploiting previous results on Markovian dynamics and fluctuation theorems, we study the consequences of memory effects on single realizations of nonequilibrium processes within an open system approach. The entropy production along single trajectories for forward and backward processes is obtained with the help of a recently proposed classical-like non-Markovian stochastic unravelling, which is demonstrated to lead to a correction of the standard entropic fluctuation theorem. This correction is interpreted as resulting from the interplay between the information extracted from the system through measurements and the flow of information from the environment to the open system: Due to memory effects single realizations of a dynamical process are no longer independent, and their correlations fundamentally affect the behavior of entropy fluctuations.Comment: 7 pages, 1 figur

Information processing in biological molecular machines

Biological molecular machines are bi-functional enzymes that simultaneously catalyze two processes: one providing free energy and second accepting it. Recent studies show that most protein enzymes have a rich dynamics of stochastic transitions between the multitude of conformational substates that make up their native state. It often manifests in fluctuating rates of the catalyzed processes and the presence of short-term memory resulting from the preference of selected conformations. For any stochastic protein machine dynamics we proved a generalized fluctuation theorem that leads to the extension of the second law of thermodynamics. Using them to interpret the results of random walk on a complex model network, we showed the possibility of reducing free energy dissipation at the expense of creating some information stored in memory. The subject of our analysis is the time course of the catalyzed processes expressed by sequences of jumps at random moments of time. Since similar signals can be registered in the observation of real systems, all theses of the paper are open to experimental verification. From a broader physical point of view, the division of free energy into the operation and organization energies is worth emphasizing. Information can be assigned a physical meaning of a change in the value of both these functions of state.Comment: The manuscript contains 14 pages, 7 figure

On the second fluctuation--dissipation theorem for nonequilibrium baths

Baths produce friction and random forcing on particles suspended in them. The relation between noise and friction in (generalized) Langevin equations is usually referred to as the second fluctuation-dissipation theorem. We show what is the proper nonequilibrium extension, to be applied when the environment is itself active and driven. In particular we determine the effective Langevin dynamics of a probe from integrating out a steady nonequilibrium environment. The friction kernel picks up a frenetic contribution, i.e., involving the environment's dynamical activity, responsible for the breaking of the standard Einstein relation

Quantum channels and their entropic characteristics

One of the major achievements of the recently emerged quantum information theory is the introduction and thorough investigation of the notion of quantum channel which is a basic building block of any data-transmitting or data-processing system. This development resulted in an elaborated structural theory and was accompanied by the discovery of a whole spectrum of entropic quantities, notably the channel capacities, characterizing information-processing performance of the channels. This paper gives a survey of the main properties of quantum channels and of their entropic characterization, with a variety of examples for finite dimensional quantum systems. We also touch upon the "continuous-variables" case, which provides an arena for quantum Gaussian systems. Most of the practical realizations of quantum information processing were implemented in such systems, in particular based on principles of quantum optics. Several important entropic quantities are introduced and used to describe the basic channel capacity formulas. The remarkable role of the specific quantum correlations - entanglement - as a novel communication resource, is stressed.Comment: review article, 60 pages, 5 figures, 194 references; Rep. Prog. Phys. (in press

Extreme event statistics of daily rainfall: Dynamical systems approach

We analyse the probability densities of daily rainfall amounts at a variety of locations on the Earth. The observed distributions of the amount of rainfall fit well to a q-exponential distribution with exponent q close to q=1.3. We discuss possible reasons for the emergence of this power law. On the contrary, the waiting time distribution between rainy days is observed to follow a near-exponential distribution. A careful investigation shows that a q-exponential with q=1.05 yields actually the best fit of the data. A Poisson process where the rate fluctuates slightly in a superstatistical way is discussed as a possible model for this. We discuss the extreme value statistics for extreme daily rainfall, which can potentially lead to flooding. This is described by Frechet distributions as the corresponding distributions of the amount of daily rainfall decay with a power law. On the other hand, looking at extreme event statistics of waiting times between rainy days (leading to droughts for very long dry periods) we obtain from the observed near-exponential decay of waiting times an extreme event statistics close to Gumbel distributions. We discuss superstatistical dynamical systems as simple models in this context.Comment: 10 pages, 15 figures. Replaced by final version published in J.Phys.