The Big World of Nanothermodynamics

TL;DR

Nanothermodynamics extends classical thermodynamics to small systems, incorporating finite-size effects and subdivision potential, enabling better understanding of relaxation, critical phenomena, and noise in nanomaterials.

Contribution

This paper introduces nanothermodynamics with subdivision potential and nanocanonical ensemble, advancing the theoretical framework for finite-size systems and their thermodynamic behavior.

Findings

Predicts stretched-exponential relaxation in heterogeneous regions

Provides nonlinear correction to Boltzmann's factor for better modeling

Explains the origin of 1/f noise in materials

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.