1210.3015 (Purushottam D. Dixit)

A maximum entropy thermodynamics for small systems    [PDF]

Purushottam D. Dixit

We present a maximum entropy based approach to analyze small systems. For small systems, noting that to construct a predictive organizational principle, the mean values of observables as well as the fluctuations around the mean values are important, we employ a superstatistical approach: The probability distribution $P(i)$ for the phase space ${i}$ is expressed as a marginal distribution summed over varying external parameters $\bar \alpha$ that characterize the interaction of the system with the surrounding bath. The distribution $P(\bar \alpha)$ of the external parameters itself is estimated by maximizing its entropy. We test our hierarchical idea on a simple harmonic oscillator strongly coupled to a bath of Lennard-Jones particles. The estimated distribution $P(r)$ of the position $r$ of the oscillator does depend on the information that is used to construct it and distributions with more information describe the experimental system better. Moreover, the traditional `canonical ensemble' distribution emerges as a limiting case of a much richer class of maxEnt distributions. Future directions and other connections with traditional statistical mechanics are discussed.

View original: http://arxiv.org/abs/1210.3015