arXiv subjects

Pierre Gaspard

Publications and source records attributed to Pierre Gaspard.

At least 37 records · Page 2Linked to original sources

arXiv2020

Stochastic approach to entropy production in chemical chaos

Methods are presented to evaluate the entropy production rate in stochastic reactive systems. These methods are shown to be consistent with known results from nonequilibrium chemical thermodynamics. Moreover, it is proved that the time average of the entropy production rate can be decomposed into the contributions of the cycles obtained from the stoichiometric matrix in both stochastic processes and deterministic systems. These methods are applied to a complex reaction network constructed on the basis of Roessler's reinjection principle and featuring chemical chaos.

nlin.CD↗

arXiv2020

Molecular theory of Langevin dynamics for active self-diffusiophoretic colloids

Active colloidal particles that are propelled by a self-diffusiophoretic mechanism are often described by Langevin equations that are either postulated on physical grounds or derived using the methods of fluctuating hydrodynamics. While these descriptions are appropriate for colloids of micrometric and larger size, they will break down for very small active particles. A fully microscopic derivation of Langevin equations for self-diffusiophoretic particles powered by chemical reactions catalyzed asymmetrically by the colloid is given in this paper. The derivation provides microscopic expressions for the translational and rotational friction tensors, as well as reaction rate coefficients appearing in the Langevin equations. The diffusiophoretic force and torque are expressed in terms of nonequilibrium averages of fluid fields that satisfy generalized transport equations. The results provide a description of active motion on small scales where descriptions in terms of coarse grained continuum fluid equations combined with boundary conditions that account for the presence of the colloid may not be appropriate.

cond-mat.stat-mech↗

arXiv2020

Comment on "Validity of path thermodynamics in reactive systems''

The paper by Malek Mansour and Garcia [Phys. Rev. E 101, 052135 (2020)] is shown to be based on misconceptions in the stochastic formulation of chemical thermodynamics in reactive systems. Their erroneous claims, asserting that entropy production cannot be correctly evaluated using path probabilities whenever the reactive system involves more than one elementary reaction leading to the same composition changes, are refuted.

cond-mat.stat-mech↗

arXiv2020

Microscopic approach to the macrodynamics of matter with broken symmetries

A unified set of hydrodynamic equations describing condensed phases of matter with broken continuous symmetries is derived using a generalization of the statistical-mechanical approach based on the local equilibrium distribution. The dissipativeless and dissipative parts of the current densities and the entropy production are systematically deduced in this approach by expanding in powers of the gradients of the macrofields. Green-Kubo formulas are obtained for all the transport coefficients. The results apply to both crystalline solids and liquid crystals. The consequences of microreversibility and spatial symmetries are investigated, leading to the prediction of cross effects resulting from Onsager-Casimir reciprocal relations.

cond-mat.stat-mech↗

arXiv2020

Counting statistics and microreversibility in stochastic models of transistors

Multivariate fluctuation relations are established in three stochastic models of transistors, which are electronic devices with three ports and thus two coupled currents. In the first model, the transistor has no internal state variable and particle exchanges between the ports is described as a Markov jump process with constant rates. In the second model, the rates linearly depend on an internal random variable, representing the occupancy of the transistor by charge carriers. The third model has rates nonlinearly depending on the internal occupancy. For the first and second models, finite-time multivariate fluctuation relations are also established giving insight into the convergence towards the asymptotic form of multivariate fluctuation relations in the long-time limit. For all the three models, the transport properties are shown to satisfy Onsager's reciprocal relations in the linear regime close to equilibrium as well as their generalizations holding in the nonlinear regimes farther away from equilibrium, as a consequence of microreversibility.

cond-mat.stat-mech↗

arXiv2020

Active matter, microreversibility, and thermodynamics

Active matter, comprising many active agents interacting and moving in fluids or more complex environments, is a commonly occurring state of matter in biological and physical systems. By its very nature active matter systems exist in nonequilibrium states. In this paper the active agents are small Janus colloidal particles that use chemical energy provided by chemical reactions occurring on their surfaces for propulsion through a diffusiophoretic mechanism. As a result of interactions among these colloids, either directly or through fluid velocity and concentration fields, they may act collectively to form structures such as dynamic clusters. A general nonequilibrium thermodynamics framework for the description of such systems is presented that accounts for both self-diffusiophoresis and diffusiophoresis due to external concentration gradients, and is consistent with microreversibility. It predicts the existence of a reciprocal effect of diffusiophoresis back onto the reaction rate for the entire collection of colloids in the system, as well as the existence of a clustering instability that leads to nonequilibrium inhomogeneous system states.

cond-mat.soft↗

arXiv2020

Template-directed growth of copolymers

The theory of multistate template-directed reversible copolymerization is developed by extending the method based on iterated function systems to matrices, taking into account the possibility of multiple activation states instead of a single one for the growth process. In this extended theory, the mean growth velocity is obtained with an iterated matrix function system and the probabilities of copolymer sequences are given by matrix products defined along the template. The theory allows us to understand the effects of template heterogeneity, which include a fractal distribution of local growth velocities far enough from equilibrium, and a regime of sublinear growth in time close to equilibrium.

physics.bio-ph↗

arXiv2019

The 2019 Motile Active Matter Roadmap

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of active matter in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines.

cond-mat.soft↗

arXiv2019

Microreversibility, nonequilibrium response, and Euler's polynomials

Microreversibility constrains the fluctuations of the nonequilibrium currents that cross an open system. This can be seen from the so-called fluctuation relations, which are a direct consequence of microreversibility. Indeed, the latter are known to impose time-reversal symmetry relations on the statistical cumulants of the currents and their responses at arbitrary orders in the deviations from equilibrium. Remarkably, such relations have been recently analyzed by means of Euler's polynomials. Here we show that fluctuation relations can actually be explicitly written in terms of the constant terms of these particular polynomials. We hence demonstrate that Euler's polynomials are indeed fundamentally rooted in fluctuation relations, both in the absence and the presence of an external magnetic field.

cond-mat.stat-mech↗

arXiv2019

Microreversibility and driven Brownian motion with hydrodynamic long-time correlations

A nonequilibrium fluctuation theorem is established for a colloidal particle driven by an external force within the hydrodynamic theory of Brownian motion, describing hydrodynamic memory effects such as the t^(-3/2) power-law decay of the velocity autocorrelation function. The generalized Langevin equation is obtained for the general case of slip boundary conditions between the particle and the fluid. The Gaussian probability distributions for the particle to evolve in position-velocity space are deduced. It is proved that the joint probability distributions of forward and time-reversed paths have a ratio depending only on the work performed by the external force and the fluid temperature, in spite of the nonMarkovian character of the generalized Langevin process.

cond-mat.stat-mech↗

arXiv2019

The stochastic motion of self-thermophoretic Janus particles

Langevin equations for the self-thermophoretic dynamics of Janus motors partially coated with an absorbing layer that is heated by a radiation field are presented. The derivation of these equations is based on fluctuating hydrodynamics and radiative heat transfer theory involving stochastic equations for bulk phases and surface processes that are consistent with microscopic reversibility. Expressions for the self-thermophoretic force and torque for arbitrary slip boundary conditions are obtained. The overdamped Langevin equations for the colloid displacement and radiative heat transfer provide expressions for the self-thermophoretic velocity and its reciprocal contribution where an external force can influence the radiative heat transfer. A nonequilibrium fluctuation formula is also derived and shows how the probability density of the Janus particle displacement and radiation energy transfer during the time interval [0,t] are related to the mechanical and thermal affinities that characterize the nonequilibrium system state.

cond-mat.stat-mech↗

arXiv2019

Multistate reversible copolymerization of nonMarkovian chains under low conversion conditions

The reversible kinetics of copolymerization is solved analytically for the multistate mechanism proposed by B. D. Coleman and T. G. Fox [J. Chem. Phys. 38, 1065 (1963)] under low conversion conditions where the concentrations of monomeric species are chemostatted and stay constant in time. Although the rates of this mechanism only depends on the currently attached or detached monomer, the growing macromolecular chain forms a nonMarkovian sequence that is characterized by matrices associated with every monomeric unit composing the sequence. These matrices are obtained by solving the kinetic equations and they determine the growth velocity of the copolymers, the statistical properties of its possible sequences, as well as the thermodynamics of the copolymerization process.

physics.chem-ph↗

arXiv2018

Microreversibility, fluctuations, and nonlinear transport in transistors

We present a stochastic approach for charge transport in transistors. In this approach, the electron and hole densities are governed by diffusion-reaction stochastic differential equations satisfying local detailed balance and the electric field is determined with the Poisson equation. The approach is consistent with the laws of electricity, thermodynamics, and microreversibility. In this way, the signal amplifying effect of transistors is verified under their working conditions. We also perform the full counting statistics of the two electric currents coupled together in transistors and we show that the fluctuation theorem holds for their joint probability distribution. Similar results are obtained including the displacement currents. In addition, the Onsager reciprocal relations and their generalizations to nonlinear transport properties deduced from the fluctuation theorem are numerically shown to be satisfied.

cond-mat.stat-mech↗

arXiv2018

Single particle motion and collective dynamics in Janus motor systems

The single-particle and collective dynamics of systems comprising Janus motors, solvent and reactive solute species maintained in nonequilibrium states are investigated. Reversible catalytic reactions with the solute species take place on the catalytic faces of the motors, and the nonequilibrium states are established by imposing either constant-concentration reservoirs that feed and remove reactive species, or through out-of-equilibrium fluid phase reactions. We consider general intermolecular interactions between the Janus motor hemispheres and the reactive species. For single motors, we show that the reaction rate depends nonlinearly on an applied external force when the system is displaced far from equilibrium. We also show that a finite-time fluctuation formula derived for fixed catalytic particles describes the nonequilibrium reactive fluctuations of moving Janus motors. Simulation of the collective dynamics of small ensembles of Janus motors with reversible kinetics under nonequilibrium conditions are carried out and the spatial and orientational correlations of dynamic cluster states are discussed. The conditions leading to the instability of the homogeneous motor distribution and the onset of nonequilibrium dynamical clustering are described.

cond-mat.soft↗

arXiv2018

Thermodynamics and statistical mechanics of chemically-powered synthetic nanomotors

Colloidal motors without moving parts can be propelled by self-diffusiophoresis, coupling molecular concentration gradients generated by surface chemical reactions to the velocity slip between solid Janus particles and the surrounding fluid solution. The interfacial properties involved in this propulsion mechanism can be described by nonequilibrium thermodynamics and statistical mechanics, disclosing the fundamental role of microreversibility in the coupling between motion and reaction. Among other phenomena, the approach predicts that propulsion by fuel consumption has the reciprocal effect of fuel synthesis by mechanical action.

cond-mat.stat-mech↗

arXiv2018

Microreversibility and nonequilibrium response theory in magnetic fields

For open systems subjected to external magnetic fields, relations between the statistical cumulants of their fluctuating currents and their response coefficients are established at arbitrary orders in the deviations from equilibrium, as a consequence of microreversibility. These relations are systematically deduced from the extension of the fluctuation relation for this class of systems, and analyzed by using methods developed in [M. Barbier and P. Gaspard, J. Phys. A: Math. Theor. 51 (2018) 355001]. We unambiguously identify, among the statistical cumulants and their nonequilibrium responses, which of these quantities are independent and thus left unspecified by the fluctuation relation, i.e. by microreversibility. We also find the explicit expression of the dependent quantities in terms of the independent ones by means of coefficients of Euler polynomials.

cond-mat.stat-mech↗

arXiv2018

Finite-time fluctuation theorem for diffusion-influenced surface reactions on spherical and Janus catalytic particles

A finite-time fluctuation theorem for the diffusion-influenced surface reaction A <=> B is investigated for spherical and Janus catalytic particles. The finite-time rates and thermodynamic force are analytically calculated by solving diffusion equations with the special boundary conditions of the finite-time fluctuation theorem. Theory is compared with numerical simulations carried out with two different methods: a random walk algorithm and multiparticle collision dynamics.

cond-mat.stat-mech↗

arXiv2018

Finite-time fluctuation theorem for diffusion-influenced surface reactions

A finite-time fluctuation theorem is proved for the diffusion-influenced surface reaction A<->B in a domain with any geometry where the species A and B undergo diffusive transport between the reservoir and the catalytic surface. A corresponding finite-time thermodynamic force or affinity is associated with the symmetry of the fluctuation theorem. The time dependence of the affinity and the reaction rates characterizing the stochastic process can be expressed analytically in terms of the solution of deterministic diffusion equations with specific boundary conditions.

cond-mat.stat-mech↗