No abstract

A fluctuation theorem is proved for the macroscopic currents of a system in a nonequilibrium steady state, by using Schnakenberg network theory. The theorem can be applied, in particular, in reaction systems where the affinities or thermodynamic forces are defined globally in terms of the cycles of the graph associated with the stochastic process describing the time evolution.

We use a recently proved fluctuation theorem for the currents to develop the response theory of nonequilibrium phenomena. In this framework, expressions for the response coefficients of the currents at arbitrary orders in the thermodynamic forces or affinities are obtained in terms of the fluctuations of the cumulative currents and remarkable relations are obtained which are the consequences of microreversibility beyond Onsager reciprocity relations.

We consider general fluctuating copolymerization processes, with or without underlying templates. The dissipation associated with these nonequilibrium processes turns out to be closely related to the information generated. This shows in particular how information acquisition results from the interplay between stored patterns and dynamical evolution in nonequilibrium environments. In addition, we apply these results to the process of DNA replication.DNA replication ͉ entropy production ͉ nonequilibrium fluctuations ͉ self-organization T he origin of biological information is one of the major challenges for our understanding of living organisms. Since the discovery of DNA, the biochemical support for the storage of genetic information has been known. DNA is a copolymer that keeps the memory of information on the living organism in its structure. This molecular structure is stable at ambient temperatures because of the binding energy between the nucleotides, allowing the heredity of genetic information across generations. As observed in vitro in evolution experiments on RNA and viruses (1, 2), the processing of biological information can be discussed in terms of the dynamics of populations associated with the different possible genetic sequences, the populations evolving by replications and mutations into quasispecies (3, 4). Such population dynamics are nonequilibrium processes where dissipation is compensated by energy supply, and the entropy produced by dissipation is evacuated to the environment of these open systems. However, this view relies on macroscopic concepts such as population size, which are largely separated from the nanoscale of the genetic sequences. Moreover, observations reveal that biological systems have structures and functions at every scale down to the molecular level, and the understanding of their origin is a challenge.Actually, the information in DNA copolymers is processed and replicated by mechanisms taking place at the molecular level in the presence of thermal fluctuations. These fluctuations are due to the random motion of the atoms and molecules composing DNA, the transcription or replication machinery, and their environment. In this regard, biological information processing is ruled by the statistical laws of motion and thermodynamics. At thermodynamic equilibrium, the principle of detailed balance implies that no information can be spontaneously processed or generated because each random motion is statistically balanced by the corresponding reverse motion. Therefore, equilibrium is the stage of erratic motion where information generation is highly improbable.Recently, it has been shown that nonequilibrium fluctuating systems present a time asymmetry in which the typical random paths followed by the system during its time evolution turn out to be more probable than their time reversal (5-8). The remarkable result is that this temporal ordering of nonequilibrium fluctuations is the consequence of the second law of thermodynamics. This phenomenon explains that dynamical order can be ...

The fluctuation theorem for the currents is applied to several mesoscopic systems on the basis of Schnakenberg's network theory, which allows one to verify its conditions of validity. A graph is associated with the master equation ruling the random process and its cycles can be used to obtain the thermodynamic forces or affinities corresponding to the nonequilibrium constraints. This provides a method to define the independent currents crossing the system in nonequilibrium steady states and to formulate the fluctuation theorem for the currents. This result is applied to out-ofequilibrium diffusion in a chain, to a biophysical model of ion channels in a membrane, as well as to electronic transport in mesoscopic circuits made of several tunnel junctions. In this later, we show that the generalizations of Onsager's reciprocity relations to the nonlinear response coefficients also hold.