Role of Hidden Slow Degrees of Freedom in the Fluctuation Theorem

Abstract

The validity of the fluctuation theorem for entropy production as deduced from the observation of trajectories implicitly requires that all slow degrees of freedom are accessible. We experimentally investigate the role of hidden slow degrees of freedom in a system of two magnetically coupled driven colloidal particles. The apparent entropy production based on the observation of just one particle obeys a fluctuation theorem-like symmetry with a slope of 1 in the short time limit. For longer times, we find a constant slope, but different from 1. We present theoretical arguments for a generic linear behavior both for small and large apparent entropy production but not necessarily throughout. By fine-tuning experimental parameters, such an intermediate nonlinear behavior can indeed be recovered in our system as well.

Thermodynamic inference based on coarse-grained data or noisy measurements

“…The modifications of fluctuation relations due to coarse-graining have been studied by a number of authors following the original theoretical work of Rahav et al [11] and motivated by various experimental systems such as manipulated colloids [12,13], granular systems [14], quantum dot devices [9,15], molecular motors [16,17], and single biopolymer molecules [4,18,19]. For instance, for molecular motors, the issue of coarse-graining is central, since only their position is typically available as a function of time experimentally.…”

Hidden entropy production by fast variables

“…Such systems can be coarse-grained in terms of so-called mesostates which refer to a set of microscopic configurations connected via fast processes [4,8]. The coarse-graining is also necessary if some degrees of freedom are inaccessible due to e.g., a resolution limit of measurement devices [9,12]. The coarse-graining naturally raises questions on the formulation of effective thermodynamics and on the extent to which the thermodynamic laws are valid.…”

“…When one studies a thermodynamic system, a coarsegrained description may be necessary [3][4][5][6][7][8][9][10][11][12]. Suppose that some transition rates among microscopic configurations are much faster than the others.…”

Energetics of synchronization in coupled oscillators rotating on circular trajectories

“…In general, phase equations may be more complicated, where the natural frequency is phase-dependent and the coupling function is no longer the function of the phase difference (see Eqs. (26) and (27) below as an example). However, applying standard techniques in nonlinear dynamics such as cycle averaging under a suitable variable transformation, we can reduce such phase equations into the same form as Eqs.…”

“…1). Both are coupled, e.g., hydrodynamically [13,14,19] or magnetically [27,28]. We assume that their dynamical behavior can be described by the following phase equationṡ…”