Biomedical subjects

Pierre Gaspard

Publications and source records attributed to Pierre Gaspard.

10 recordsLinked to original sources

PubMed2006

Fluctuation theorems and the nonequilibrium thermodynamics of molecular motors.

The fluctuation theorems for the currents and the dissipated work are considered for molecular motors which are driven out of equilibrium by chemical reactions. Because of the molecular fluctuations, these nonequilibrium processes are described by stochastic models based on a master equation. Analytical expressions are derived for the fluctuation theorems, allowing us to obtain predictions on the work dissipated in the motor as well as on its rotation near and far from thermodynamic equilibrium. We show that the fluctuation theorems provide a method to determine the affinity or thermodynamic force driving the motor. This affinity is given in terms of the free enthalpy of the chemical reactions. The theorems are applied to the F1 rotary motor which turns out to be a stiff system typically functioning in the nonlinear regime of nonequilibrium thermodynamics. We show that this nonlinearity confers a robustness to the functioning of the molecular motor.

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PubMed2005

Entropy production in diffusion-reaction systems: the reactive random Lorentz gas.

We report the study of a random Lorentz gas with a reaction of isomerization A<==>B between two colors of moving particles elastically bouncing on hard disks. The reaction occurs when the moving particles collide on catalytic disks, which constitute a fraction of all the disks. Under dilute-gas conditions, the reaction-diffusion process is ruled by two coupled Boltzmann-Lorentz equations for the distribution functions of the colors. The macroscopic reaction-diffusion equations with cross-diffusion terms induced by the chemical reaction are derived from the kinetic equations. We use an H theorem of the kinetic theory in order to derive a macroscopic entropy depending on the gradients of color densities and which has a non-negative entropy production in agreement with the second law of thermodynamics.

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PubMed2005

Non-Markovian stochastic Schrödinger equations in different temperature regimes: a study of the spin-boson model.

Stochastic Schrodinger equations are used to describe the dynamics of a quantum open system in contact with a large environment, as an alternative to the commonly used master equations. We present a study of the two main types of non-Markovian stochastic Schrodinger equations, linear and nonlinear ones. We compare them both analytically and numerically, the latter for the case of a spin-boson model. We show in this paper that two linear stochastic Schrodinger equations, derived from different perspectives by Diosi, Gisin, and Strunz [Phys. Rev. A 58, 1699 (1998)], and Gaspard and Nagaoka [J. Chem. Phys. 13, 5676 (1999)], respectively, are equivalent in the relevant order of perturbation theory. Nonlinear stochastic Schrodinger equations are in principle more efficient than linear ones, as they determine solutions with a higher weight in the ensemble average which recovers the reduced density matrix of the quantum open system. However, it will be shown in this paper that for the case of a spin-boson system and weak coupling, this improvement does only occur in the case of a bath at high temperature. For low temperatures, the sampling of realizations of the nonlinear equation is practically equivalent to the sampling of the linear ones. We study further this result by analyzing, for both temperature regimes, the driving noise of the linear equations in comparison to that of the nonlinear equations.

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PubMed2004

Fluctuation theorem for nonequilibrium reactions.

A fluctuation theorem is derived for stochastic nonequilibrium reactions ruled by the chemical master equation. The theorem is expressed in terms of the generating and large-deviation functions characterizing the fluctuations of a quantity which measures the loss of detailed balance out of thermodynamic equilibrium. The relationship to entropy production is established and discussed. The fluctuation theorem is verified in the Schlögl model of far-from-equilibrium bistability.

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PubMed2003

Quantum master equation for a system influencing its environment.

A perturbative quantum master equation is derived for a system interacting with its environment, which is more general than the ones derived before. Our master equation takes into account the effect of the energy exchanges between the system and the environment and the conservation of energy in the finite total system. This master equation describes relaxation mechanisms in isolated nanoscopic quantum systems. In its most general form, this equation is non-Markovian and a Markovian version of it rules the long-time relaxation. We show that our equation reduces to the Redfield equation in the limit where the energy of the system does not affect the density of state of its environment. This master equation and the Redfield one are applied to a spin-environment model defined in terms of random matrices and compared with the solutions of the exact von Neumann equation. The comparison proves the necessity to allow energy exchange between the subsystem and the environment in order to correctly describe the relaxation in an isolated nanoscopic total system.

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PubMed2003

Spin relaxation in a complex environment.

We report the study of a model of a two-level system interacting in a nondiagonal way with a complex environment described by Gaussian orthogonal random matrices (GORM). The effect of the interaction on the total spectrum and its consequences on the dynamics of the two-level system is analyzed. We show the existence of a critical value of the interaction, depending on the mean level spacing of the environment, above which the dynamics is self-averaging and closely obey a master equation for the time evolution of the observables of the two-level system. Analytic results are also obtained in the strong coupling regimes. We finally study the equilibrium values of the two-level system population and show under which condition it thermalizes to the environment temperature.

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PubMed2003

Lyapunov exponent of ion motion in microplasmas.

Dynamical chaos is studied in the Hamiltonian motion of ions confined in a Penning trap and forming so-called microplasmas. The dynamical chaos of the ion motion is characterized by the maximum Lyapunov exponent. Results are reported on the dependence of this exponent on the energy of the system, on the number of ions, as well as on the geometry of the trap. Different dynamical regimes are characterized from the crystalline state to a strongly chaotic regime, and to quasiharmonic motion in the external potential of the trap. Across these regimes, the Lyapunov exponent increases, reaches a maximum value, and decreases as a function of energy. Besides, the maximum value of the Lyapunov exponent increases as a function of the number of ions.

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PubMed2002

Deterministic diffusion in flower-shaped billiards.

We propose a flower-shaped billiard in order to study the irregular parameter dependence of chaotic normal diffusion. Our model is an open system consisting of periodically distributed obstacles in the shape of a flower, and it is strongly chaotic for almost all parameter values. We compute the parameter dependent diffusion coefficient of this model from computer simulations and analyze its functional form using different schemes, all generalizing the simple random walk approximation of Machta and Zwanzig. The improved methods we use are based either on heuristic higher-order corrections to the simple random walk model, on lattice gas simulation methods, or they start from a suitable Green-Kubo formula for diffusion. We show that dynamical correlations, or memory effects, are of crucial importance in reproducing the precise parameter dependence of the diffusion coefficent.

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PubMed1993

What is the role of chaotic scattering in irreversible processes?

We study kinetic properties of simple mechanical models of deterministic diffusion like the scattering of a point particle in a billiard of Lorentz type and the multibaker area-preserving map. We show how dynamical chaos and, in particular, chaotic scattering are related to the transport property of diffusion. Moreover, we show that the Liouvillian dynamics of the multibaker map can be decomposed into the eigenmodes of diffusive relaxation associated with the Ruelle resonances of the Perron-Frobenius operator.

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PubMed1992

Investigation of the Lorentz gas in terms of periodic orbits.

The diffusion constant and the Lyapunov exponent for the spatially periodic Lorentz gas are evaluated numerically in terms of periodic orbits. A symbolic description of the dynamics reduced to a fundamental domain is used to generate the shortest periodic orbits. Applied to a dilute Lorentz gas with finite horizon, the theory works well, but for the dense Lorentz gas the convergence is hampered by the strong pruning of the admissible orbits.

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