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Entropy 2015, 17(1), 52-73; doi:10.3390/e17010052

The Big World of Nanothermodynamics

Department of Physics, Arizona State University, Tempe, AZ 85287-1504, USA
Received: 11 November 2014 / Accepted: 23 December 2014 / Published: 31 December 2014
(This article belongs to the Special Issue Nanothermodynamics)
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Abstract

Nanothermodynamics extends standard thermodynamics to facilitate finite-size effects on the scale of nanometers. A key ingredient is Hill’s subdivision potential that accommodates the non-extensive energy of independent small systems, similar to how Gibbs’ chemical potential accommodates distinct particles. Nanothermodynamics is essential for characterizing the thermal equilibrium distribution of independently relaxing regions inside bulk samples, as is found for the primary response of most materials using various experimental techniques. The subdivision potential ensures strict adherence to the laws of thermodynamics: total energy is conserved by including an instantaneous contribution from the entropy of local configurations, and total entropy remains maximized by coupling to a thermal bath. A unique feature of nanothermodynamics is the completely-open nanocanonical ensemble. Another feature is that particles within each region become statistically indistinguishable, which avoids non-extensive entropy, and mimics quantum-mechanical behavior. Applied to mean-field theory, nanothermodynamics gives a heterogeneous distribution of regions that yields stretched-exponential relaxation and super-Arrhenius activation. Applied to Monte Carlo simulations, there is a nonlinear correction to Boltzmann’s factor that improves agreement between the Ising model and measured non-classical critical scaling in magnetic materials. Nanothermodynamics also provides a fundamental mechanism for the 1/f noise found in many materials. View Full-Text
Keywords: small-system thermodynamics; maximum entropy; thermodynamic ensembles; thermal fluctuations; stretched-exponential relaxation; non-Arrhenius activation; critical scaling; 1/f noise; Gibbs’ paradox; statistics of indistinguishable particles small-system thermodynamics; maximum entropy; thermodynamic ensembles; thermal fluctuations; stretched-exponential relaxation; non-Arrhenius activation; critical scaling; 1/f noise; Gibbs’ paradox; statistics of indistinguishable particles
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Chamberlin, R.V. The Big World of Nanothermodynamics. Entropy 2015, 17, 52-73.

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