1,720,993 research outputs found
Dissipation-Time Uncertainty Relation
Full text linkWe show that the entropy production rate bounds the rate at which physical processes can be performed in stochastic systems far from equilibrium. In particular, we prove the fundamental tradeoff S ̇eT≥kB between the entropy flow S ̇e into the reservoirs and the mean time T to complete any process whose time-reversed is exponentially rarer. This dissipation-time uncertainty relation is a novel form of speed limit: The smaller the dissipation, the larger the time to perform a process
Nonisothermal fluctuating hydrodynamics and Brownian motion
No full textThe classical theory of Brownian dynamics follows from coarse graining the underlying linearized fluctuating hydrodynamics of the solvent. We extend this procedure to globally nonisothermal conditions, requiring only a local thermal equilibration of the solvent. Starting from the conservation laws, we establish the stochastic equations of motion for the fluid momentum fluctuations in the presence of a suspended Brownian particle. These are then contracted to the nonisothermal generalized Langevin description of the suspended particle alone, for which the coupling to stochastic temperature fluctuations is found to be negligible under typical experimental conditions
Nonequilibrium temperature response for stochastic overdamped systems
Full text linkThe thermal response of nonequilibrium systems requires the knowledge of concepts that go beyond entropy production. This is showed for systems obeying overdamped Langevin dynamics, either in steady states or going through a relaxation process. Namely, we derive the linear response to perturbations of the noise intensity, mapping it onto the quadratic response to a constant small force. The latter, displaying divergent terms, is explicitly regularised with a novel path-integral method. The nonequilibrium equivalents of heat capacity and thermal expansion coefficient are two applications of this approach, as we show with numerical examples
Generalized virial equation for nonlinear multiplicative Langevin dynamics: Application to laser-cooled atoms
No full textThe virial theorem, and the equipartition theorem in the case of quadratic degrees of freedom, are handy constraints on the statistics of equilibrium systems. Their violation is instrumental in determining how far from equilibrium a driven system might be. We extend the virial theorem to nonequilibrium conditions for Langevin dynamics with nonlinear friction and multiplicative noise. In particular, we generalize it for confined laser-cooled atoms in the semiclassical regime. The resulting relation between the lowest moments of the atom position and velocity allows to measure in experiments how dissipative the cooling mechanism is. Moreover, its violation can reveal the departure from a strictly harmonic confinement or from the semiclassical regime
Information Thermodynamics of Turing Patterns
No full textWe set up a rigorous thermodynamic description of reaction-diffusion systems driven out of equilibrium by time-dependent space-distributed chemostats. Building on the assumption of local equilibrium, nonequilibrium thermodynamic potentials are constructed exploiting the symmetries of the chemical network topology. It is shown that the canonical (resp. semigrand canonical) nonequilibrium free energy works as a Lyapunov function in the relaxation to equilibrium of a closed (resp. open) system, and its variation provides the minimum amount of work needed to manipulate the species concentrations. The theory is used to study analytically the Turing pattern formation in a prototypical reaction-diffusion system, the one-dimensional Brusselator model, and to classify it as a genuine thermodynamic nonequilibrium phase transition
Chemical cloaking
Full text linkHiding an object in a chemical gradient requires one to suppress the distortions it would naturally cause on it. To do so, we propose a strategy based on coating the object with a chemical reaction-diffusion network which can act as an active cloaking device. By controlling the concentration of some species in its immediate surrounding, the chemical reactions redirect the gradient as if the object was not there. We also show that a substantial fraction of the energy required to cloak can be extracted from the chemical gradient itself
Strong current response to slow modulation: A metabolic case-study
Full text linkWe study the current response to periodic driving of a crucial biochemical reaction network, namely, substrate inhibition. We focus on the conversion rate of substrate into product under time-varying metabolic conditions, modeled by a periodic modulation of the product concentration. We find that the system exhibits a strong nonlinear response to small driving frequencies both for the mean time-averaged current and for the fluctuations. For the first, we obtain an analytic formula by coarse-graining the original model to a solvable one. The result is nonperturbative in the modulation amplitude and frequency. We then refine the picture by studying the stochastic dynamics of the full system using a large deviation approach that allows us to show the resonant effect at the level of the time-averaged variance and signal-to-noise ratio. Finally, we discuss how this nonequilibrium effect may play a role in metabolic and synthetic networks
Thermodynamics of chemical waves
No full textChemical waves constitute a known class of dissipative structures emerging in reaction-diffusion systems. They play a crucial role in biology, spreading information rapidly to synchronize and coordinate biological events. We develop a rigorous thermodynamic theory of reaction diffusion systems to characterize chemical waves. Our main result consists of defining the proper thermodynamic potential of the local dynamics as a nonequilibrium free energy density and establishing its balance equation. This enables us to identify the dynamics of the free energy, of the dissipation, and of the work spent to sustain the wave propagation. Two prototypical classes of chemical waves are examined. From a thermodynamic perspective, the first is sustained by relaxation toward equilibrium and the second by nonconservative forces generated by chemostats. We analytically study step-like waves, called wavefronts, using the Fisher-Kolmogorov equation as a representative of the first class and oscillating waves in the Brusselator model as a representative of the second. Given the fundamental role of chemical waves as message carriers in biosystems, our thermodynamic theory constitutes an important step toward an understanding of information transfers and processing in biology
About the role of chaos and coarse graining in statistical mechanics
No full textWe discuss the role of ergodicity and chaos for the validity of statistical laws. In particular we explore the basic aspects of chaotic systems (with emphasis on the finite-resolution) on systems composed of a huge number of particles
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