Strong Coupling and Nonextensive Thermodynamics

Miguel, Rodrigo de; Rubı́, J. M.

doi:10.3390/e22090975

Cited by 7 publications

(7 citation statements)

References 30 publications

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“…However, in contrast to Hill’s purely thermodynamic approach, the subdivision potential has now a thermostatistical interpretation in terms of the temperature-dependence of the effective Hamiltonian ( 17 ). The method of statistical mechanics at strong coupling has recently been used to analyze interfacial phenomena, easily producing laws shown to be valid at the nanoscale [ 3 ].…”

Section: Strong Coupling and Hill’s Nanothermodynamicsmentioning

confidence: 99%

“…In other cases, surroundings significantly affect the properties of systems, and external interactions need to be taken into account. Systems subject to the latter scenario may be referred to as small, where small is not an attribute determined by the system’s sheer size, but rather by how the size compares to the range of the interactions affecting the system [ 1 , 2 , 3 ].…”

Section: Introductionmentioning

confidence: 99%

“…This framework is based on the formulation of a Hamiltonian of mean force , which accounts for environmental perturbations on the small system of interest [ 30 ]. This thermostatistical approach has recently been applied to describe nanomechanical systems [ 31 ], nanoscale interfacial phenomena [ 3 ] and the advent of negative thermophoresis [ 32 ].…”

Section: Introductionmentioning

confidence: 99%

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

Miguel

Rubı́

2020

Nanomaterials

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We review and show the connection between three different theories proposed for the thermodynamic treatment of systems not obeying the additivity ansatz of classical thermodynamics. In the 1950s, Landsberg proposed that when a system comes into contact with a heat bath, its energy levels are redistributed. Based on this idea, he produced an extended thermostatistical framework that accounts for unknown interactions with the environment. A decade later, Hill devised his celebrated nanothermodynamics, where he introduced the concept of subdivision potential, a new thermodynamic variable that accounts for the vanishing additivity of increasingly smaller systems. More recently, a thermostatistical framework at strong coupling has been formulated to account for the presence of the environment through a Hamiltonian of mean force. We show that this modified Hamiltonian yields a temperature-dependent energy landscape as earlier suggested by Landsberg, and it provides a thermostatistical foundation for the subdivision potential, which is the cornerstone of Hill’s nanothermodynamics.

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Section: Strong Coupling and Hill’s Nanothermodynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Miguel

Rubı́

2020

Nanomaterials

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“…2 Yet a water droplet may well be thought of as large. 3 This issue was addressed by the celebrated physical chemist Terrel L. Hill in the early 1960s, when he generalized classical thermodynamics to describe small systems. 4,5 Hill considered a homogeneous macroscopic system at equilibrium and abstractly subdivided it into very small subsystems.…”

Section: Introductionmentioning

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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“…Srong interactions and correlations with the bath, however, cause serious ambiguities in construction of system thermodynamic quantities, such as entropy and internal energy [5,7]. Many different approaches have been tried to construct a reduced thermodynamic theory for strongly coupled small systems, both classical [5][6][7][8][9][10][11][12][13][14], and quantum [17][18][19][20][21][22][23][24][25], and there has been no sign of convergence yet on the opinions. Jarzynski [5] proposed to remove these ambiguities for the classical case by fixing the definition of system volume, and developed a theory encompassing both the classical thermodynamics and stochastic thermodynamics.…”

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confidence: 99%

Strong Coupling Thermodynamics and Stochastic Thermodynamics from the Unifying Perspective of Time-Scale Separation

Ding,

Tu,

Xing

2021

Preprint

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Assuming time-scale separation, a simple and unified theory of thermodynamics and stochastic thermodynamics is constructed for small classical systems strongly interacting with its environment in a controllable fashion. The total Hamiltonian is decomposed into a bath part and a system part, the latter being the Hamiltonian of mean force. Both the conditional equilibrium of bath and the reduced equilibrium of the system are described by canonical ensemble theories with respect to their own Hamiltonians. The bath free energy is independent of the system variables and the control parameter. Furthermore, the weak coupling theory of stochastic thermodynamics becomes applicable almost verbatim, even if the interaction and correlation between the system and its environment are strong and varied externally. Finally, this TSS-based approach also leads to some new insights about the origin of the second law of thermodynamics.

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Strong Coupling and Nonextensive Thermodynamics

Cited by 7 publications

References 30 publications

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

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

Rayleigh–Schrödinger Perturbation Theory and Nonadditive Thermodynamics

Strong Coupling Thermodynamics and Stochastic Thermodynamics from the Unifying Perspective of Time-Scale Separation

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