2015/03/05 by Purushottam D. Dixit, Dixit, Purushottam D. · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Biological Physics (physics.bio-ph) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1503.01808
openalex publication_date 2015/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Gibbs and Boltzmann definitions of temperature agree only in the macroscopic limit. The ambiguity in identifying the equilibrium temperature of a finite sized `small' system exchanging energy with a bath is usually understood as a limitation of conventional statistical mechanics. We interpret this ambiguity as resulting from a stochastically fluctuating temperature coupled with the phase space variables giving rise to a broad temperature distribution. With this ansatz, we develop the equilibrium statistics and dynamics of small systems. Numerical evidence using an analytically tractable model shows that the effects of temperature fluctuations can be detected in equilibrium and dynamical properties of the phase space of the small system. Our theory generalizes statistical mechanics to small systems relevant to biophysics and nanotechnology.