Statistical Mechanics at Strong Coupling: A Bridge between Landsberg’s Energy Levels and Hill’s Nanothermodynamics

Miguel, Rodrigo de; Rubı́, J. M.

doi:10.3390/nano10122471

Cited by 10 publications

(6 citation statements)

References 33 publications

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“…It was first proposed by Rushbrooke and later refined by Elcock and Landsberg in the late 1950s . More recently, this idea has resurfaced in a framework known as statistical mechanics at strong coupling . , Incidentlly, the framework of temperature-dependent energy levels is acknowledged in Pathria’s landmark tektbook in statistical mechanics (see ref , chapter 3, footnote 1).…”

Section: Thermally Induced Spectrum Perturbationsmentioning

confidence: 99%

Rayleigh–Schrödinger Perturbation Theory and Nonadditive Thermodynamics

Miguel

2023

J. Phys. Chem. B

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Physical chemists reconcile the empirical theory of classical thermodynamics with the quantum nature of matter and energy when they recover thermodynamics from a statistical mechanical treatment of the individual particles’ quantized eigenspectrum. The conclusion is that, when systems are very large collections of particles, interactions between adjacent systems are comparatively negligible, resulting in an additive thermodynamic framework where the energy of a composite system AB may be expressed as the sum of the individual energies of subsystems A and B. This powerful theory is consistent with quantum theory, and it accurately describes the macroscopic properties of sufficiently large systems subject to comparatively short-ranged interactions. Nevertheless, classical thermodynamics has its limitations. Its main drawback is the theory’s failure to accurately describe systems not sufficiently large for the aforementioned interaction to be neglected. This shortcoming was addressed by the celebrated chemist Terrell L. Hill in the 1960s when he generalized classical thermodynamics by adding a phenomenological energy term to describe systems not captured by the additivity ansatz (i.e., AB ≠ A + B) of classical thermodynamics. Despite its elegance and success, Hill’s generalization mostly remained a specialist tool rather than becoming part of the standard chemical thermodynamics corpus. A probable reason is that, in contrast to the classical large-system case, Hill’s small-system framework does not reconcile with a thermostatistical treatment of quantum mechanical eigenenergies. In this work we show that, by introducing a temperature-dependent perturbation in the particles’ energy spectrum, Hill’s generalized framework is in fact recovered with a simple thermostatistical analysis accessible to physical chemists.

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Section: Thermally Induced Spectrum Perturbationsmentioning

confidence: 99%

Rayleigh–Schrödinger Perturbation Theory and Nonadditive Thermodynamics

Miguel

2023

J. Phys. Chem. B

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“…Terrell L. Hill proposed a first thermodynamic approach for dealing with small systems 1 , 2 , named now as nanothermodynamics 3 , which is attracting much renewed attention with the advent of nanoscience and nanotechnology. Its foundation and various fundamental aspects are currently under active scrutiny 4 – 18 . Hill’s nanothermodynamics is based on a replica trick and a new thermodynamic function, subdivision potential, which is conjugated with replica number.…”

Section: Introductionmentioning

confidence: 99%

Nanoscale thermodynamics needs the concept of a disjoining chemical potential

Dong

2023

Nat Commun

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Disjoining pressure was discovered by Derjaguin in 1930’s, which describes the difference between the pressure of a strongly confined fluid and the corresponding one in a bulk phase. It has been revealed recently that the disjoining pressure is at the origin of distinct differential and integral surface tensions for strongly confined fluids. Here we show how the twin concept, disjoining chemical potential, arises in a reminiscent way although it comes out eighty years later. This twin concept advances our understanding of nanoscale thermodynamics. Ensemble-dependence (or environment-dependence) is one hallmark of thermodynamics of small systems. We show that integral surface tension is ensemble-dependent while differential surface tension is not. Moreover, two generalized Gibbs-Duhem equations involving integral surface tensions are derived, as well as two additional adsorption equations relating surface tensions to adsorption-induced strains. All the results obtained in this work further evidence that an approach alternative of Hill’s nanothermodynamics is possible, by extending Gibbs surface thermodynamics instead of resorting to Hill’s replica trick. Moreover, we find a compression-expansion hysteresis without any underlying phase transition.

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“…The last two papers [9,10] are special. The only experimental paper in this issue is provided by Men'shikov et al [9].…”

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confidence: 99%

“…Is there an alternative route, simpler than that of Hill, to nanothermodynamics? Rodrigo de Miguel and J. Miguel Rubi [10] propose this in their study on "Statistical Mechanics at Strong Coupling: A Bridge between Landsberg's Energy Levels and Hill's Nanothermodynamics". They review and show the connection between three theories, including Hill's, proposed for the thermodynamic treatment of systems that do not obey the additivity ansatz of classical thermodynamics.…”

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confidence: 99%