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Condensed Matter > Statistical Mechanics

Title:A maximum entropy thermodynamics for small systems

Abstract: We present a maximum entropy based approach to analyze small systems. In small systems, the fluctuations around the mean values of observables are not negligible. Consequently, the probability $P(i)$ of the state space ${i}$ of the system cannot be described by a unique set of Lagrange multipliers. We employ a superstatistical approach: The probability distribution $P(i)$ for the phase space ${i}$ is expressed as a marginal distribution summed over the variation in the Lagrange multipliers $\bar ζ$ that characterize the interaction of the system with the surrounding bath. The joint distribution $P(i, \bar ζ)$ is estimated by maximizing its entropy.
We test the development 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. 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.
Subjects: Statistical Mechanics (cond-mat.stat-mech)
Cite as: arXiv:1210.3015 [cond-mat.stat-mech]
  (or arXiv:1210.3015v2 [cond-mat.stat-mech] for this version)

Submission history

From: Purushottam Dixit [view email]
[v1] Wed, 10 Oct 2012 19:52:19 UTC (244 KB)
[v2] Tue, 30 Oct 2012 14:05:07 UTC (490 KB)
[v3] Wed, 7 Nov 2012 18:18:46 UTC (488 KB)
[v4] Tue, 13 Nov 2012 20:51:17 UTC (489 KB)
[v5] Wed, 21 Nov 2012 17:56:41 UTC (485 KB)
[v6] Tue, 12 Feb 2013 18:50:46 UTC (399 KB)
[v7] Thu, 11 Apr 2013 01:53:20 UTC (278 KB)