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1732 results in Physical chemistry

Page 3 of 87

  • 6 - Path Probabilities, Temporal Disorder, and Irreversibility

  • Pierre Gaspard, Université Libre de Bruxelles
  • Book:
    The Statistical Mechanics of Irreversible Phenomena
    Published online:
    14 July 2022
    Print publication:
    28 July 2022, pp 257-295

  • Summary

    The stroboscopic observation of stochastic processes records the history of the system as paths, which can be characterized by their probability distribution. Temporal disorder results in the exponential decay of the path probabilities as the observational time increases. The mean decay rate defines the so-called entropy per unit time, which measures the amount of temporal disorder in the process. At equilibrium, the probabilities of a path and its time reversal are equal by the principle of detailed balance. In contrast, they differ under nonequilibrium conditions, which is the manifestation of irreversibility. Remarkably, the ratio of the probabilities of opposite paths has a logarithm obeying a fluctuation relation and having a mean value related to the thermodynamic entropy production rate. These results show that temporal ordering can be generated in nonequilibrium processes as a corollary of the second law. These considerations shed new light on Landauer’s principle.

  • 8 - Effusion Processes

  • Pierre Gaspard, Université Libre de Bruxelles
  • Book:
    The Statistical Mechanics of Irreversible Phenomena
    Published online:
    14 July 2022
    Print publication:
    28 July 2022, pp 319-332

  • Summary

    Effusion is one of the most elementary kinetic processes, to which the concepts of nonequilibrium statistical mechanics can be applied. Remarkably, the stationary probability distribution can be exactly constructed as a so-called Poisson suspension, explicitly showing that time reversal is broken at the statistical level of description under nonequilibrium conditions. The multivariate fluctuation relation for the energy and particle currents can be directly deduced from the underlying microscopic dynamics. Moreover, temporal disorder and its nonequilibrium time asymmetry can be fully characterized and shown to be related to the thermodynamic entropy production. The multivariate fluctuation relation can also be applied to mass separation by effusion.

  • 3 - Hydrodynamics

  • Pierre Gaspard, Université Libre de Bruxelles
  • Book:
    The Statistical Mechanics of Irreversible Phenomena
    Published online:
    14 July 2022
    Print publication:
    28 July 2022, pp 99-146

  • Summary

    Hydrodynamics is deduced from the microscopic dynamics using local equilibrium probability distributions for multicomponent normal fluids and the phases of matter with broken continuous symmetries such as crystals and liquid crystals. The Nambu–Goldstone modes resulting from continuous symmetry breaking are identified at the microscopic level of description. The entropy and the entropy production are introduced within the local equilibrium approach in agreement with the second law of thermodynamics. The Green–Kubo formulas are obtained for all the transport coefficients associated with the linear response properties, including the cross-coupling effects satisfying the Onsager–Casimir reciprocal relations as a consequence of microreversibility. The boundary conditions due to the presence of interfaces are discussed, as well as the hydrodynamic long-time tails and their consequences, especially, in low-dimensional systems.

The Statistical Mechanics of Irreversible Phenomena
  • Pierre Gaspard
  • Published online:
    14 July 2022
    Print publication:
    28 July 2022
  • This book provides a comprehensive and self-contained overview of recent progress in nonequilibrium statistical mechanics, in particular, the discovery of fluctuation relations and other time-reversal symmetry relations. The significance of these advances is that nonequilibrium statistical physics is no longer restricted to the linear regimes close to equilibrium, but extends to fully nonlinear regimes. These important new results have inspired the development of a unifying framework for describing both the microscopic dynamics of collections of particles, and the macroscopic hydrodynamics and thermodynamics of matter itself. The book discusses the significance of this theoretical framework in relation to a broad range of nonequilibrium processes, from the nanoscale to the macroscale, and is essential reading for researchers and graduate students in statistical physics, theoretical chemistry and biological physics.

Nonlinear Optical Polarization Analysis in Chemistry and Biology
  • Garth J. Simpson
  • Published online:
    04 May 2017
    Print publication:
    24 March 2017
  • This rigorous yet accessible guide presents a molecular-based description of nonlinear optical polarization analysis of chemical and biological assemblies. It includes discussion of the most common nonlinear optical microscopy and interfacial measurements used for quantitative analysis, specifically second harmonic generation (SHG), two-photon excited fluorescence (2PEF), vibrational sum frequency generation (SFG), and coherent anti-Stokes Raman spectroscopy/stimulated Raman spectroscopy (CARS/SRS). A linear algebra mathematical framework is developed, allowing step-wise systematic connections to be made between the observable measurements and the molecular response. Effects considered include local field corrections, the molecular orientation distribution, rotations between the molecular frame, the local frame and the laboratory frame, and simplifications from molecular and macromolecular symmetry. Specific examples are provided throughout the book, working from the common and relatively simple case studies through to the most general scenarios.

Page 3 of 87