arXiv subjects

Pierre Gaspard

Publications and source records attributed to Pierre Gaspard.

At least 19 recordsLinked to original sources

arXiv2026

Kinetics of template-directed multistate copolymerization

We consider processes of template-directed multistate copolymerization by molecular machines such as polymerases or ribosomes, having multiple states of conformation or activation. We show that the kinetic equations of these processes can be exactly solved for the mean growth velocity, the sequence probabilities of the grown copy, and the local probabilities and fractions of monomeric units in the copy. Asymptotically, in the long-time limit, the kinetic equations are solved with a matrix factorization ansatz in terms of a backward iteration, forming an iterated matrix function system, and a complementary forward iteration, both running along the template sequence. The iterative method is very significantly faster than usual computational methods, as demonstrated with a numerical example.

q-bio.QM↗

arXiv2026

Kinetics of multistate DNA polymerases

In the present paper, we apply the iterative mathematical method previously developed for the kinetics of template-directed multistate copolymerization to the kinetics of DNA replication by polymerases having multiple structural states. In particular, we study a two-state kinetic model for the T7 DNA polymerase. We obtain the mean velocity for the growth of the copy along the template, the error probability of DNA replication by the polymerase, and the local probabilities of base-pair formation along the template sequence. Furthermore, we show that the iterative method is more than a million times faster than usual numerical simulation methods. Results are also obtained in the approximation of homogenization of template heterogeneities.

q-bio.QM↗

arXiv2026

Chargaff's second parity rule and the kinetics of DNA replication

This paper presents the study of a DNA replication model grounded in the biochemical kinetics of DNA polymerases, which copy each DNA strand into a complementary strand, except for rare point-like mutations caused by nucleotide substitution errors. Numerical simulations of many successive replications, starting from an arbitrary initial DNA sequence, show that the fractions of mono- and oligonucleotides converge toward compliance with Chargaff's second parity rule. The theoretical framework developed for this multireplication process demonstrates that the near-equalities of complementary nucleotide fractions arise from two key features: (1) the dominant role of base-pair complementarity in replication kinetics and (2) the low intrinsic error rate of DNA polymerases. Together, these two features yield a robust mechanistic basis for Chargaff's second parity rule. These considerations explain the existence of deviations with respect to the predictions of models assuming no-strand-bias conditions.

q-bio.QM↗

arXiv2025

From the thermodynamics of irreversible processes to dissipative structures and active matter

A historical perspective is presented on thermodynamics from the pioneering contributions by Carnot and Clausius to recent advances on active matter. Non-equilibrium thermodynamics develops from the identification of the irreversible processes contributing to entropy production in various types of materials and systems. These processes include friction, viscosity, heat and electric conductions, diffusion, reactions, and more. In 1954, Glansdorff and Prigogine formulated a general evolution criterion, which led to the theory of dissipative structures like chemical clocks, reaction-diffusion patterns, and convection patterns. Non-equilibrium statistical mechanics provides the microscopic foundations for the thermodynamics of irreversible processes.

physics.gen-ph↗

arXiv2025

Dynamic structure factor of a monatomic cubic crystal

The spectral function of density fluctuations, also known as the dynamic structure factor, of a monatomic cubic crystal with vacancies is derived from the macroscopic equations describing transport in crystalline solids. The resonances of the spectral function are identified as a Brillouin doublet of sound propagation, a central Rayleigh peak of heat diffusion, as for perfect crystals, and another central sharp peak associated with vacancy diffusion. Analytical expressions for the heat and vacancy diffusivities, speeds of sound, and sound damping coefficients are obtained. The theoretical results are compared to molecular dynamics simulations of a face-centered cubic crystal of hard spheres.

cond-mat.stat-mech↗

arXiv2025

The non-equilibrium thermodynamics of active suspensions

Active suspensions composed of self-propelled colloidal particles are considered. Their propulsion of is generated by chemical reactions occurring by heterogeneous catalysis and diffusiophoresis coupling the concentration gradients of reacting molecular species to the fluid velocity. By this mechanism, chemical free energy is transduced into mechanical motion. The non-equilibrium thermodynamics of such active suspensions is developed by explicitly taking into account the internal degrees of freedom of active particles, which are the Eulerian angles specifying their orientation. Accordingly, the distribution function of colloidal particles is defined in the six-dimensional configuration space of their position and their orientation, which fully characterises polar, nematic, and higher orientational orders in the active system. The local Gibbs and Euler thermodynamic relations are expressed in terms of the colloidal distribution function, the dynamics of which is ruled by a six-dimensional local conservation equation. All the processes contributing to the entropy production rate are derived from the local conservation and kinetic equations for colloids, molecular species, mass, linear momentum, and energy, identifying their thermodynamic forces, also called affinities, and their dissipative current densities. The non-equilibrium constitutive relations are obtained using the Curie symmetry principle and the Onsager-Casimir reciprocal relations based on microreversibility. In this way, all the mechanochemical coupling coefficients are completely determined for isothermal, incompressible, dilute suspensions composed of spherical Janus particles on the basis of the interfacial properties between the fluid solution and the solid particles and chemohydrodynamics. The complete expression of the entropy production rate is established for such active systems.

cond-mat.soft↗

arXiv2025

The stress tensor of dilute active colloidal suspensions

The stress tensor is calculated for dilute active suspensions composed of colloidal Janus particles propelled by self-diffusiophoresis and powered by a chemical reaction. The Janus particles are assumed to be spherical and made of catalytic and non-catalytic hemispheres. The chemical reaction taking place on the catalytic part of each Janus particle generates local molecular concentration gradients at the surface of the particle and, thus, an interfacial velocity slippage between the fluid and the solid particle, which is the propulsion mechanism of self-diffusiophoresis. In the dilute-system limit, the contributions of the suspended particles to the stress tensor are calculated by solving the chemohydrodynamic equations for the fluid velocity and the molecular concentrations around every Janus particle considered as isolated and far apart from each other. The results are the following. First, the well-known Einstein formula for the effective shear viscosity of colloidal suspensions is recovered, including the effect of a possible Navier slip length. Next, two further contributions are obtained, which depend on the molecular concentrations of the fuel and product species of the chemical reaction and on the orientation of the Janus particles. The second contribution is caused by simple diffusiophoresis, which already exists in passive suspensions with global concentration gradients and no reaction. The third contribution is due to the self-diffusiophoresis generated by the chemical reaction, which arises in active suspensions. The calculation gives quantitative predictions, which depend on the constitutive properties of the fluid and the fluid-solid interfaces, as well as on the geometry of the Janus particles.

cond-mat.soft↗

arXiv2024

Dynamical response and time correlation functions in random quantum systems

Time-dependent response and correlation functions are studied in random quantum systems composed of infinitely many parts without mutual interaction and defined with statistically independent random matrices. The latter are taken within the three Wigner-Dyson universality classes. In these systems, the response functions are shown to be exactly given by statistical averages over the random-matrix ensemble. Analytical results are obtained for the time dependence of the mean response and correlation functions at zero and positive temperatures. At long times, the mean correlation functions are shown to have a power-law decay for GOE at positive temperatures, but for GUE and GSE at zero temperature. Otherwise, the decay is much faster in time. In relation to these power-law decays, the associated spectral densities have a dip around zero frequency. The diagrammatic method is developed to obtain higher-order response functions and the third-order response function is explicitly calculated. The response to impulsive perturbations is also considered. In addition, the quantum fluctuations of the correlation function in individual members of the ensemble are characterised in terms of their probability distribution, which is shown to change with the temperature.

cond-mat.stat-mech↗

arXiv2024

Vacancy diffusion and the hydrodynamics of crystals

The hydrodynamics of crystals with vacancies is developed on the basis of local-equilibrium thermodynamics, where the chemical potential of vacancies plays a key role together with a constraint relating the concentration of vacancies to the density of mass and the strain tensor. The microscopic foundations are established, leading to Green-Kubo and Einstein-Helfand formulas for the transport coefficients, including the vacancy conductivities and the coefficients of vacancy thermodiffusion. As a consequence of having introduced the chemical potential of vacancies, a relationship is obtained between the conductivities and the Fickian diffusion coefficients for the vacancies. The macroscopic equations are linearized around equilibrium to deduce the dispersion relations of the eight hydrodynamic modes. The theoretical predictions are confirmed by numerical simulations of the hard-sphere crystal with vacancies. The study explicitly shows that the eighth hydrodynamic mode of nonperfect monatomic crystals is indeed a mode of vacancy diffusion.

cond-mat.stat-mech↗

arXiv2023

Elastic and transport coefficients of the perfect hard-sphere crystal from the poles of the hydrodynamic spectral functions

The elastic and transport coefficients of a perfect face-centered cubic crystal of hard spheres are computed from the poles of the dynamic structure factor and of the spectral functions of transverse momentum density fluctuations. For such crystals, the relevant coefficients are the three isothermal elastic constants $(C_{11}^T,C_{12}^T,C_{44}^T)$, the heat conductivity $κ$, and the three viscosities $(η_{11},η_{12},η_{44})$ (in Voigt's notations), which are directly computed using molecular dynamics simulations. The elastic and transport coefficients are then compared to the values of the same coefficients obtained with the method of Helfand moments, showing good agreement and providing strong support for the microscopic hydrodynamic theory of perfect crystals based on the local-equilibrium approach.

cond-mat.stat-mech↗

arXiv2023

Hydrodynamic correlation and spectral functions of perfect cubic crystals

We investigate the collective dynamics of the perfect cubic crystal by deriving from the hydrodynamic equations the time-dependent correlation and the spectral functions characterizing the fluctuations of mass and momentum densities. We show that the seven hydrodynamic modes of the perfect crystal can be identified from the resonances of these spectral functions. The comparison with those of a fluid is discussed. Using the numerical values of the thermodynamic, elastic, and transport coefficients computed in our previous paper [J. Mabillard and P. Gaspard, arXiv:2311.00757 (2023)] for a system of hard spheres, the theoretical expressions for the correlation and spectral functions are compared to the same functions directly computed using molecular dynamics simulations. The excellent agreement between theory and simulation provides strong support for the microscopic hydrodynamic theory of perfect crystals based on the local-equilibrium approach. This work sheds light on the fundamental mechanisms governing the collective behavior of matter in the solid state.

cond-mat.stat-mech↗

arXiv2023

Hydrodynamic properties of the perfect hard-sphere crystal: Microscopic computations with Helfand moments

Within the framework of the local-equilibrium approach, the equilibrium and nonequilibrium properties relevant to the hydrodynamics of the perfect hard-sphere crystal are obtained with molecular dynamics simulations using the Helfand moments associated with momentum and energy transports. Since this crystal is face-centered cubic, the hydrodynamic properties we consider are the hydrostatic pressure, the isothermal bulk modulus, the specific heat capacities and their ratio, the three isothermal elastic constants $(C_{11}^T,C_{12}^T,C_{44}^T)$, the heat conductivity, and the three viscosities $(η_{11},η_{12},η_{44})$ (in Voigt's notations). These properties are computed as a function of the particle density. The pressure and the transport coefficients diverge near the close-packing density, as the collision frequency per particle does.

cond-mat.stat-mech↗

arXiv2023

Poles of hydrodynamic spectral functions and Einstein-Helfand formulas for transport coefficients

The local-equilibrium approach to transport processes is related to the approach based on time-dependent correlation functions and their associated spectral functions characterizing the equilibrium fluctuations of particle, momentum and other densities. On the one hand, the transport coefficients are calculated with the Einstein-Helfand formulas derived in the local-equilibrium approach. On the other hand, the poles of the spectral functions at complex frequencies give the damping rates of the hydrodynamic modes. Since these rates also depend on the transport coefficients, their values can be compared to the predictions of the local-equilibrium approach. This comparison is systematically carried out for the hard-sphere fluid by computing numerically the transport coefficients, the spectral functions, and their poles as a function of the wave number in the hydrodynamic limit. The study shows the consistency between the two approaches for the determination of the transport properties.

cond-mat.stat-mech↗

arXiv2023

Comment on "Validity of path thermodynamic description of reactive systems: Microscopic simulations''

The claims by Baras, Garcia, and Malek Mansour [Phys. Rev. E 107, 014106 (2023)] on the validity of path thermodynamics are ill founded and contradict well known results. Following up on a previous comment, I show that, for both models of chemical reaction networks considered in the aforementioned paper, path thermodynamics yields values of the entropy production rates fully consistent with those expected from standard chemical thermodynamics in the large-system limit.

cond-mat.stat-mech↗

arXiv2022

Quantum local-equilibrium approach to dissipative hydrodynamics

The macroscopic hydrodynamic equations are derived for many-body systems in the local-equilibrium approach, using the Schrödinger picture of quantum mechanics. In this approach, statistical operators are defined in terms of microscopic densities associated with the fundamentally conserved quantities and other slow modes possibly emerging from continuous symmetry breaking, as well as macrofields conjugated to these densities. Functional identities can be deduced, allowing us to identify the reversible and dissipative parts of the mean current densities, to obtain general equations for the time evolution of the conjugate macrofields, and to establish the relationship to projection-operator methods. The entropy production is shown to be nonnegative by applying the Peierls-Bogoliubov inequality to a quantum integral fluctuation theorem. Using the expansion in the gradients of the conjugate macrofields, the transport coefficients are given by Green-Kubo formulas and the entropy production rate can be expressed in terms of quantum Einstein-Helfand formulas, implying its nonnegativity in agreement with the second law of thermodynamics. The results apply to multicomponent fluids and can be extended to condensed matter phases with broken continuous symmetries.

cond-mat.stat-mech↗

arXiv2021

A robust transition to homochirality in complex chemical reaction networks

Homochirality, i.e. the dominance across all living matter of one enantiomer over the other among chiral molecules, is thought to be a key step in the emergence of life. Building on ideas put forward by Frank and many others, we proposed recently one such mechanism in G. Laurent et al., PNAS (2021) based on the properties of large out of equilibrium chemical networks. We showed that in such networks, a phase transition towards an homochiral state is likely to occur as the number of chiral species in the system becomes large or as the amount of free energy injected into the system increases. This paper aims at clarifying some important points in that scenario, not covered by our previous work. We first analyze the various conventions used to measure chirality, introduce the notion of chiral symmetry of a network, and study its implications regarding the relative chiral signs adopted by different groups of molecules. We then propose a generalization of Frank's model for large chemical networks, which we characterize completely using methods of random matrices. This analysis can be extended to sparse networks, which shows that the emergence of homochirality is a robust transition.

cond-mat.stat-mech↗

arXiv2021

Nonequilibrium statistical mechanics of crystals

The local equilibrium approach previously developed by the Authors [J. Mabillard and P. Gaspard, J. Stat. Mech. (2020) 103203] for matter with broken symmetries is applied to crystalline solids. The macroscopic hydrodynamics of crystals and their local thermodynamic and transport properties are deduced from the microscopic Hamiltonian dynamics. In particular, the Green-Kubo formulas are obtained for all the transport coefficients. The eight hydrodynamic modes and their dispersion relation are studied for general and cubic crystals. In the same twenty crystallographic classes as those compatible with piezoelectricity, cross effects coupling transport between linear momentum and heat or crystalline order are shown to split the degeneracy of damping rates for modes propagating in opposite generic directions.

cond-mat.stat-mech↗

arXiv2021

Emergence of homochirality in large molecular systems

The selection of a single molecular handedness, or homochirality across all living matter, is a mystery in the origin of life. Frank's seminal model showed in the fifties how chiral symmetry breaking can occur in non-equilibrium chemical networks. However, an important shortcoming in this classic model is that it considers a small number of species, while there is no reason for the prebiotic system, in which homochirality first appeared, to have had such a simple composition. Furthermore, this model does not provide information on what could have been the size of the molecules involved in this homochiral prebiotic system. Here, we show that large molecular systems are likely to undergo a phase transition towards a homochiral state, as a consequence of the fact that they contain a large number of chiral species. Using chemoinformatics tools, we quantify how abundant are chiral species in the chemical universe of all possible molecules of a given length. Then, we propose that Frank's model should be extended to include a large number of species, in order to possess the transition towards homochirality as confirmed by numerical simulations. Finally, using random matrix theory, we prove that large non-equilibrium reaction networks possess a generic and robust phase transition towards a homochiral state.

cond-mat.stat-mech↗