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Superstatistics in nanoscale electrochemical systems.

Vladimir García-Morales¹, Katharina Krischer

¹Institute for Advanced Study, Technische Universität München, Lichtenbergstrasse 2a, D-85748 Garching, Germany. vmorales@ph.tum.de

Proceedings of the National Academy of Sciences of the United States of America

|November 23, 2011

Summary

Stochastic electrochemical reactions on nanosized electrodes become non-Markovian when driven by voltage. These systems exhibit a superstatistics of Tsallis

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Area of Science:

Electrochemistry
Statistical Mechanics
Nanotechnology

Background:

Stochastic electrochemical reaction steps on nanosized electrodes are typically Markovian in the absence of external driving forces.
External driving, such as applied voltage, can introduce non-Markovian behavior and complex correlations in nanoscale electrochemical systems.

Purpose of the Study:

To investigate the statistical behavior of externally driven stochastic electrochemical reactions on nanosized electrodes.
To characterize the non-Markovian dynamics using superstatistics and Tsallis indices.
To explore the relationship between nanoscale electrochemical systems and generalized statistical mechanics.

Main Methods:

Development and application of the electrochemical master equation to model stochastic reaction steps.
Analysis of stochastic trajectories to determine the distribution of Tsallis' q indices.
Investigation of the thermodynamic limit to recover Boltzmann-Gibbs thermostatistics.

Main Results:

Externally driven nanoscale electrochemical systems exhibit non-Markovian behavior.
These systems obey a superstatistics characterized by a superposition of Tsallis' q indices.
Boltzmann-Gibbs thermostatistics are recovered in the thermodynamic limit, and the superstatistical entropic form is additive.

Conclusions:

Superstatistics provide a framework to describe non-Markovian nanoscale electrochemical systems.
The distribution of Tsallis' q indices can be directly calculated from a mesoscopic master equation without ad hoc assumptions.
This approach offers a way to analyze complex correlations in microstates within a superstatistical perspective.