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Kinetics and thermodynamics of reversible polymerization in closed systems ; ; Esposito, Massimiliano et al in New Journal of Physics (2015), 17(8), Motivated by a recent study on the metabolism of carbohydrates in bacteria, we study the kinetics and thermodynamics of two classic models for reversible polymerization, one preserving the total polymer ... [more ▼] Motivated by a recent study on the metabolism of carbohydrates in bacteria, we study the kinetics and thermodynamics of two classic models for reversible polymerization, one preserving the total polymer concentration and the other one not. The chemical kinetics is described by rate equations following the mass-action law. We consider a closed system and nonequilibrium initial conditions and show that the system dynamically evolves towards equilibrium where a detailed balance is satisfied. The entropy production during this process can be expressed as the time derivative of a Lyapunov function. When the solvent is not included in the description and the dynamics conserves the total concentration of polymer, the Lyapunov function can be expressed as a Kullback-Leibler divergence between the nonequilibrium and the equilibrium polymer length distribution. The same result holds true when the solvent is explicitly included in the description and the solution is assumed dilute, whether or not the total polymer concentration is conserved. Furthermore, in this case a consistent nonequilibrium thermodynamic formulation can be established and the out-of-equilibrium thermodynamic enthalpy, entropy and free energy can be identified. Such a framework is useful in complementing standard kinetics studies with the dynamical evolution of thermodynamic quantities during polymerization. © 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. [less ▲] Detailed reference viewed: 99 (4 UL)Inequalities Generalizing the Second Law of Thermodynamics for Transitions between Non-stationary States Verley, Gatien ; ; in Physical Review Letters (2012), 108 We discuss the consequences of a variant of the Hatano-Sasa relation in which a nonstationary distribution is used in place of the usual stationary one. We first show that this nonstationary distribution ... [more ▼] We discuss the consequences of a variant of the Hatano-Sasa relation in which a nonstationary distribution is used in place of the usual stationary one. We first show that this nonstationary distribution is related to a difference of traffic between the direct and dual dynamics. With this formalism, we extend the definition of the adiabatic and nonadiabatic entropies introduced by M. Esposito and C. Van den Broeck in Phys. Rev. Lett. 104, 090601 (2010) for the stationary case. We also obtain interesting second-law-like inequalities for transitions between nonstationary states. [less ▲] Detailed reference viewed: 60 (1 UL)Fluctuation theorems and inequalities generalizing the second law of thermodynamics out of equilibrium Verley, Gatien ; in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2012), 86 We present a general framework for systems which are prepared in a nonstationary nonequilibrium state in the absence of any perturbation and which are then further driven through the application of a time ... [more ▼] We present a general framework for systems which are prepared in a nonstationary nonequilibrium state in the absence of any perturbation and which are then further driven through the application of a time-dependent perturbation. By assumption, the evolution of the system must be described by Markovian dynamics. We distinguish two different situations depending on the way the nonequilibrium state is prepared; either it is created by some driving or it results from a relaxation following some initial nonstationary conditions. Our approach is based on a recent generalization of the Hatano-Sasa relation for nonstationary probability distributions. We also investigate whether a form of the second law holds for separate parts of the entropy production and for any nonstationary reference process, a question motivated by the work of M. Esposito et al. [ Phys. Rev. Lett. 104 090601 (2010)]. We find that although the special structure of the theorems derived in this reference is not recovered in the general case, detailed fluctuation theorems still hold separately for parts of the entropy production. These detailed fluctuation theorems contain interesting generalizations of the second law of thermodynamics for nonequilibrium systems. [less ▲] Detailed reference viewed: 60 (0 UL)Fluctuation relations and fluctuation-response for molecular motors Verley, Gatien ; in Garrido, Pedro L.; Marro, Joaquín; de los Santos, F. (Eds.) AIP Conference Proceedings (2011) Fluctuation relations are a set of remarkable relations obeyed by a large class of systems and arbitrarily far from equilibrium. It is interesting to discuss the implications of these relations for ... [more ▼] Fluctuation relations are a set of remarkable relations obeyed by a large class of systems and arbitrarily far from equilibrium. It is interesting to discuss the implications of these relations for molecular motors, which are chemically driven enzymes. These enzymes operate stochastically at the molecular level and for these reasons undergo large thermal fluctuations. Using simple ratchet models of molecular motors, the various forms of fluctuation relations can be illustrated in a simple way. In the linear regime, finite time fluctuation relations imply specific modified fluctuation-dissipation relations. [less ▲] Detailed reference viewed: 22 (1 UL)Modified fluctuation-dissipation theorem for non-equilibrium steady states and applications to molecular motors Verley, Gatien ; ; in Europhysics Letters [=EPL] (2011), 93(1), 10002 We present a theoretical framework to understand a modified fluctuation-dissipation theorem valid for systems close to non-equilibrium steady states and obeying Markovian dynamics. We discuss the ... [more ▼] We present a theoretical framework to understand a modified fluctuation-dissipation theorem valid for systems close to non-equilibrium steady states and obeying Markovian dynamics. We discuss the interpretation of this result in terms of trajectory entropy excess. The framework is illustrated on a simple pedagogical example of a molecular motor. We also derive in this context generalized Green-Kubo relations similar to the ones obtained recently in Seifert U., Phys. Rev. Lett., 104 (2010) 138101 for more general networks of biomolecular states. [less ▲] Detailed reference viewed: 67 (0 UL)Modified fluctuation-dissipation theorem for general non-stationary states and application to the Glauber-Ising chain Verley, Gatien ; ; in Journal of Statistical Mechanics : Theory and Experiment (2011), (10), 10025 In this paper, we present a general derivation of a modified fluctuation-dissipation theorem (MFDT) valid near an arbitrary non-stationary state for a system obeying Markovian dynamics. We show that the ... [more ▼] In this paper, we present a general derivation of a modified fluctuation-dissipation theorem (MFDT) valid near an arbitrary non-stationary state for a system obeying Markovian dynamics. We show that the method for deriving modified fluctuation-dissipation theorems near non-equilibrium stationary states used by Prost et al (2009 Phys. Rev. Lett. 103 090601) is generalizable to non-stationary states. This result follows from both standard linear response theory and from a transient fluctuation theorem, analogous to the Hatano?Sasa relation. We show that this modified fluctuation-dissipation theorem can be interpreted at the trajectory level using the notion of stochastic trajectory entropy in a way which is similar to what has been done recently in the case of the MFDT near non-equilibrium steady states (NESS). We illustrate this framework with two solvable examples: the first example corresponds to a Brownian particle in a harmonic trap subjected to a quench of temperature and to a time-dependent stiffness; the second example is a classic model of coarsening systems, namely the 1D Ising model with Glauber dynamics. [less ▲] Detailed reference viewed: 60 (1 UL) |
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