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A maximum entropy thermodynamics of small systems
1Biosciences Department, Brookhaven National Laboratory, Upton, New York 11973, USA. pdixit@bnl.gov
The Journal of Chemical Physics
|May 17, 2013
Summary
This study introduces a maximum entropy method to analyze complex systems, like molecules in solution. The approach accurately models the system's state space, even with significant fluctuations, by considering temperature variations.
Area of Science:
- Statistical Mechanics
- Computational Chemistry
- Physical Chemistry
Background:
- Macromolecular systems in solution exhibit significant fluctuations.
- Solute-solvent interactions intricately determine the state space probability distribution.
- Traditional canonical ensemble descriptions may require corrections for small systems.
Purpose of the Study:
- To develop a maximum entropy approach for analyzing the state space of small systems coupled to a large bath.
- To incorporate superstatistics by considering variations in the inverse temperature (β) of the solute.
- To calculate system-size corrections to the canonical ensemble.
Main Methods:
- Employing a superstatistical approach where the probability distribution P(r) is a marginal distribution over β.
- Estimating the joint distribution P(β, r) by maximizing its entropy.
- Calculating first-order system-size corrections.
Main Results:
- The maximum entropy method successfully captures the state space of a harmonic oscillator interacting with different baths (Lennard-Jones particles and water).
- The superstatistical approach effectively models systems where fluctuations are non-negligible.
- The method provides accurate descriptions beyond the standard canonical ensemble.
Conclusions:
- The developed maximum entropy and superstatistical approach is a robust tool for analyzing complex solvated systems.
- This method offers a more accurate description of the state space compared to traditional methods, especially for systems with significant fluctuations.
- Future work can explore deeper connections with established statistical mechanics principles.
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