The Big World of Nanothermodynamics

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.

22 pages, 14 figures, review

References in corpus (4)

• Beyond the Boltzmann factor for corrections to scaling in ferromagnetic materials and critical fluids
• A free-energy landscape picture and Landau theory for the dynamics of disordered materials
• Fluctuation-theory constraint for extensive entropy in Monte-Carlo simulations
• 1/f Noise from the Laws of Thermodynamics for Finite-Size Fluctuations

Cited by in corpus (9)

• Unconventional scaling at non-Hermitian critical points
• Emergence and Breaking of Duality Symmetry in Generalized Fundamental Thermodynamic Relations
• Pseudo-Phase Transitions of Ising and Baxter-Wu Models in Two-Dimensional Finite-Size Lattices
• $\mu PT$ statistical ensemble: systems with fluctuating energy, particle number, and volume
• An Ising model for the thermal and dynamic properties of supercooled liquids and the glass transition
• Quantum thermochemical engines
• Enhancing Quantum Otto Engine Performance in Generalized External Potential on Bose-Einstein Condensation Regime
• Multiscale Thermodynamics: Energy, Entropy, and Symmetry from Atoms to Bulk Behavior
• Derivation of a statistical model for classical systems obeying fractional exclusion principle