Special Issue on Nanoscale Thermodynamics

Kjelstrup, Signe

doi:10.3390/nano11030584

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“…3 below). One of the important examples of nanothermodynamics with sub-extensive effect is from the surface tension of a droplet [14].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic Behavior of Statistical Event Counting in Time: Independent and Correlated Measurements

Qian

2021

Preprint

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We introduce an entropy analysis of time series, repeated measurements of statistical observables, based on an Eulerian homogeneous degree-one entropy function Φ(t, n) of time t and number of events n. The duality of Φ, in terms of conjugate variables η = −Φ t and µ = Φ n , yields an "equation of state" (EoS) in differential form that resembles the Gibbs-Duhem relation in classical thermodynamics: tdη − ndµ = 0. For simple Poisson counting with rate r, η = r(e µ − 1). The conjugate variable η is then identified as being equal to the Hamiltonian function in a Hamilton-Jacobi equation for Φ(t, n). Applying the same logic to the entropy function of time correlated events yields a Hamiltonian as the principal eigenvalue of a matrix. For time reversible case it is the sum of a symmetric Markovian part √ πiqij/ √ πj and the conjugate variables µiδij. The eigenvector, as a posterior to the naive counting measure used as the prior, suggests a set of intrinsic characteristics of Markov states.

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“…3 below). One of the important examples of nanothermodynamics with sub-extensive effect is from the surface tension of a droplet [14].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic Behavior of Statistical Event Counting in Time: Independent and Correlated Measurements

Qian

2021

Preprint

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Emergence and Breaking of Duality Symmetry in Generalized Fundamental Thermodynamic Relations

Qian

2022

Phys. Rev. Lett.

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Special Issue on Nanoscale Thermodynamics

Abstract: This Special Issue concerns recent developments of a theory for energy conversion on the nanoscale, namely nanothermodynamics [...]

Cited by 2 publications

References 10 publications

Thermodynamic Behavior of Statistical Event Counting in Time: Independent and Correlated Measurements

Thermodynamic Behavior of Statistical Event Counting in Time: Independent and Correlated Measurements

Emergence and Breaking of Duality Symmetry in Generalized Fundamental Thermodynamic Relations

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