David Andrieux

Fluctuation theorem for currents and Schnakenberg network theory

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.

Fluctuation theorem and Onsager reciprocity relations.

The Onsager and higher-order reciprocity relations are derived from a fluctuation theorem for nonequilibrium reactions ruled by the chemical master equation. The fluctuation theorem is obtained for the generating function of the macroscopic fluxes between chemiostats maintaining the system in a nonequilibrium steady state. The macroscopic affinities associated with the fluxes are identified by graph theory. The Yamamoto-Zwanzig formulas for the reaction constants are also derived from the fluctuation theorem.

Nonequilibrium generation of information in copolymerization processes

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.

The fluctuation theorem for currents in open quantum systems

A quantum-mechanical framework is set up to describe the full counting statistics of particles flowing between reservoirs in an open system under time-dependent driving. A symmetry relation is obtained, which is the consequence of microreversibility for the probability of the nonequilibrium work and the transfer of particles and energy between the reservoirs. In some appropriate long-time limit, the symmetry relation leads to a steady-state quantum fluctuation theorem for the currents between the reservoirs. On this basis, relationships are deduced which extend the Onsager–Casimir reciprocity relations to the nonlinear response coefficients.

Entropy production and time asymmetry in nonequilibrium fluctuations.

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 Boltzmanns constant.

A fluctuation theorem for currents and non-linear response coefficients

We use a recently proved fluctuation theorem for currents to develop a response theory of non-equilibrium 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.

Fluctuation theorem for transport in mesoscopic systems

The fluctuation theorem for currents is applied to several mesoscopic systems on the basis of Schnakenbergs 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 of defining 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-of-equilibrium diffusion in a chain, to a biophysical model of ion channels in a membrane, and to electronic transport in mesoscopic circuits made of several tunnel junctions. In this latter, we show that the generalizations of Onsagers reciprocity relations to the nonlinear response coefficients also hold.

Quantum work relations and response theory

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.

Thermodynamic time asymmetry in non-equilibrium fluctuations

We here present the complete analysis of experiments on driven Brownian motion and electric noise in an RC circuit, showing that thermodynamic entropy production can be related to the breaking of time-reversal symmetry in the statistical description of these non-equilibrium systems. The symmetry breaking can be expressed in terms of dynamical entropies per unit time, one for the forward process and the other for the time-reversed process. These entropies per unit time characterize dynamical randomness, i.e., temporal disorder, in time series of the non-equilibrium fluctuations. Their difference gives the well-known thermodynamic entropy production, which thus finds its origin in the time asymmetry of dynamical randomness, alias temporal disorder, in systems driven out of equilibrium.

Fluctuation theorem and mesoscopic chemical clocks.

The fluctuation theorems for dissipation and the currents are applied to the stochastic version of the reversible Brusselator model of nonequilibrium oscillating reactions. It is verified that the symmetry of these theorems holds far from equilibrium in the regimes of noisy oscillations. Moreover, the fluctuation theorem for the currents is also verified for a truncated Brusselator model.