Introduction to Nonequilibrium Statistical Physics and Its Foundations

Rondoni, Lamberto

doi:10.1007/978-981-15-9297-3_1

Cited by 6 publications

(8 citation statements)

References 38 publications

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“…At present, one must proceed by examples, as a comprehensive theory of small and nonequilibrium systems is still missing, although notable works are being performed, see, e.g., Ref. [41] for one review.…”

Section: Discussionmentioning

confidence: 99%

Probability Turns Material: The Boltzmann Equation

Rondoni,

Di Florio

2024

Entropy

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We review, under a modern light, the conditions that render the Boltzmann equation applicable. These are conditions that permit probability to behave like mass, thereby possessing clear and concrete content, whereas generally, this is not the case. Because science and technology are increasingly interested in small systems that violate the conditions of the Boltzmann equation, probability appears to be the only mathematical tool suitable for treating them. Therefore, Boltzmann’s teachings remain relevant, and the present analysis provides a critical perspective useful for accurately interpreting the results of current applications of statistical mechanics.

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Section: Discussionmentioning

confidence: 99%

Probability Turns Material: The Boltzmann Equation

Rondoni,

Di Florio

2024

Entropy

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“…Equation ( 34) is interpreted according to the a-convention with the parameter a ∈ [0, 1]. More precisely for any real function f (x) we interpret the noise term in (34) as…”

Section: B Mesoscopic Descriptionmentioning

confidence: 99%

“…In particular, these approaches propose different laws that generalize linear constitutive relations to account for space-dependent properties of a physical system. In the problem of mass diffusion-the paradigmatic model of transport phenomena [34]-the controversy revolves around the Fick's law…”

Section: Introductionmentioning

confidence: 99%

“…However only the energy function U (x) can be interpreted as a thermodynamic potential consistently with the classical statistical mechanics and the Fick's law. The density ρ(x) of an equilibrium system must obey the Maxwell-Boltzmann distribution-a reason why the mass diffusion may be considered as a paradigmatic example of the transport phenomena [34]. This result is reproduced only for the potential U (x) in the Smoluchowski equation [47] and extends to nonequilibrium systems through Onsager's theory [54][55][56].…”

Section: Introductionmentioning

confidence: 99%

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Statistical physics of inhomogeneous transport: Unification of diffusion laws and inference from first-passage statistics

Belousov,

Hassanali,

Roldán

2021

Preprint

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Characterization of composite materials, whose properties vary in space over microscopic scales, has become a problem of broad interdisciplinary interest. In particular, estimation of the inhomogeneous transport coefficients, e.g. the diffusion coefficient or the heat conductivity which shape important processes in biology and engineering, is a challenging task. The analysis of such systems is further complicated, because two alternative formulations of the inhomogeneous transport equations exist in the literature-the Smoluchowski and Fokker-Planck equations, which are also related to the so-called Ito-Stratonovich dilemma. Using the theory of statistical physics, we show that the two formulations, usually regarded as distinct models, are physically equivalent. From this result we develop efficient estimates for the transverse space-dependent diffusion coefficient in fluids near a phase boundary. Our method requires only measurements of escape probabilities and mean exit times of molecules leaving a narrow spatial region. We test our estimates in three case studies: (i) a Langevin model of a Büttikker-Landauer ratchet; atomistic molecular-dynamics simulations of liquid-water molecules in contact with (ii) vapor and (iii) soap (surfactant) film which has promising applications in physical chemistry. Our analysis reveals that near the surfactant monolayer the mobility of water molecules is slowed down almost twice with respect to the bulk liquid. Moreover, the diffusion coefficient of water correlates with the transition from hydrophilic to hydrophobic parts of the film.

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“…Refs. [1][2][3]. While the range of applicability of the linear theory covers most phenomena occurring on the scale of our daily life, extending well beyond that scale, contemporary science and technology concern scales that are much smaller or that involve extremely large driving forces, which often exceed the linear regime.…”

Section: Introductionmentioning

confidence: 99%

Exact Response Theory for Time-Dependent and Stochastic Perturbations

Iannella,

Rondoni

2023

Entropy

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The exact, non perturbative, response theory developed within the field of non-equilibrium molecular dynamics, also known as TTCF (transient time correlation function), applies to quite general dynamical systems. Its key element is called the dissipation function because it represents the power dissipated by external fields acting on the particle system of interest, whose coupling with the environment is given by deterministic thermostats. This theory has been initially developed for time-independent external perturbations, and then it has been extended to time-dependent perturbations. It has also been applied to dynamical systems of different nature, and to oscillator models undergoing phase transitions, which cannot be treated with, e.g., linear response theory. The present work includes time-dependent stochastic perturbations in the theory using the Karhunen–Loève theorem. This leads to three different investigations of a given process. In the first, a single realization of the stochastic coefficients is fixed, and averages are taken only over the initial conditions, as in a deterministic process. In the second, the initial condition is fixed, and averages are taken with respect to the distribution of stochastic coefficients. In the last investigation, one averages over both initial conditions and stochastic coefficients. We conclude by illustrating the applicability of the resulting exact response theory with simple examples.

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Introduction to Nonequilibrium Statistical Physics and Its Foundations

Cited by 6 publications

References 38 publications

Probability Turns Material: The Boltzmann Equation

Probability Turns Material: The Boltzmann Equation

Statistical physics of inhomogeneous transport: Unification of diffusion laws and inference from first-passage statistics

Exact Response Theory for Time-Dependent and Stochastic Perturbations

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