Eur. Phys. J. B (2016) 89: 185
https://doi.org/10.1140/epjb/e2016-70242-0

Regular Article

Fluctuation theorems and 1/f noise from a simple matrix

¹ Department of Physics, Arizona State University, Tempe, AZ 85287-1504, USA
² Department of Physical Engineering, Mie University, 514-8507 Mie, Japan
³ Institute of Physics, Kazan Federal University, 420008 Kazan, Russia
⁴ Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada

^a e-mail: ralph.chamberlin@asu.edu

Received: 21 April 2016
Received in final form: 25 May 2016
Published online: 5 September 2016

Abstract

Here we present a model for a small system combined with an explicit entropy bath that is comparably small. The dynamics of the model is defined by a simple matrix, M. Each row of M corresponds to a macrostate of the system, e.g. net alignment, while the elements in the row represent microstates. The constant number of elements in each row ensures constant entropy, which allows reversible fluctuations, similar to information theory where a constant number of bits allows reversible computations. Many elements in M come from the microstates of the system, but many others come from the bath. Bypassing the bath states yields fluctuations that exhibit standard white noise; whereas with bath states the power spectral density varies as S(f) ∝ 1 /f over a wide range of frequencies, f. Thus, the explicit entropy bath is the mechanism of 1/f noise in this model. Both forms of the model match Crooks’ fluctuation theorem exactly, indicating that the theorem applies not only to infinite reservoirs, but also to finite-sized baths. The model is used to analyze measurements of 1/f-like noise from a sub-micron tunnel junction.