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.

No abstract

A universal quantum work relation is proved for isolated time-dependent Hamiltonian systems in a magnetic field as the consequence of microreversibility. This relation involves a functional of an arbitrary observable. The quantum Jarzynski equality is recovered in the case this observable vanishes. The Green-Kubo formula and the Casimir-Onsager reciprocity relations are deduced thereof in the linear response regime.Nonequilibrium work relations have recently attracted much interest [1,2]. They provide relations for the work dissipated in time-dependent driven systems, independently of the form of the driving. They are of great interest to evaluate free energies under general nonequilibrium conditions and they provide new methods to study nanosystems. In the nanoscopic world, the extension of these classical relations to quantum systems is of particular importance and different approaches have been proposed.A first scheme was introduced by Kurchan [3]. In this framework, a measurement of the system state is performed at the initial time. In the sequel, the system is perturbed by a time-dependent Hamiltonian before performing another measurement at the final time. The random work performed on the system is associated with the energy difference between the final and initial eigenstates. This setup leads to the quantum extension of Jarzynski equality and Crooks fluctuation theorem [4,5,6,7]. Another possibility is to introduce a quantum work operator which measures the energy difference [8], in which cases quantum corrections to the fluctuation theorem must be taken into account. On the other hand, quantum fluctuation theorems have been obtained in suitable limits where the dynamics admits a Markovian description, allowing in particular the applications to nonequilibrium steady states [9,10,11,12,13,14]. Yet, the connection between the quantum work relations and response theory is still an open question even in the linear regime.The purpose of the present paper is to derive a new type of work relations which involves a functional of an arbitrary observable. This generating functional can be related to another functional but averaged over the timereversed process. This new work relation turns out to be of great generality since we can recover known results such as Jarzynski equality as special cases. Furthermore, this universal work relation allows us to formulate the response theory, to derive the quantum linear response functions, the quantum Green-Kubo relations [15,16], as well as the Casimir-Onsager reciprocity relations [17,18] in the regime close to the thermodynamic equilibrium.Functional symmetry relations. We suppose that the system is described by a Hamiltonian operator H(t; B) which depends on the time t and the magnetic field B. The time-reversal operator Θ is an antilinear operator such that Θ 2 = I and which has the effect of changing the sign of all odd parameters such as magnetic fields:We first introduce the forward process. The system is initially in thermal equilibrium at the inverse temperature β...

The time-reversal symmetry of nonequilibrium fluctuations is experimentally investigated in two out-of-equilibrium systems: namely, a Brownian particle in a trap moving at constant speed and an electric circuit with an imposed mean current. The dynamical randomness of their nonequilibrium fluctuations is characterized in terms of the standard and time-reversed entropies per unit time of dynamical systems theory. We present experimental results showing that their difference equals the thermodynamic entropy production in units of Boltzmann's constant.