A topological fluctuation theorem

Abstract

Fluctuation theorems specify the non-zero probability to observe negative entropy production, contrary to a naive expectation from the second law of thermodynamics. For closed particle trajectories in a fluid, Stokes theorem can be used to give a geometric characterization of the entropy production. Building on this picture, we formulate a topological fluctuation theorem that depends only by the winding number around each vortex core and is insensitive to other aspects of the force. The probability is robust to local deformations of the particle trajectory, reminiscent of topologically protected modes in various classical and quantum systems. We demonstrate that entropy production is quantized in these strongly fluctuating systems, and it is controlled by a topological invariant. We demonstrate that the theorem holds even when the probability distributions are non-Gaussian functions of the generated heat.

Dynamic control of the Bose–Einstein-like condensation transition in scalar active matter

“…the effective temperature. For infinite systems, only one scaling regime is possible, while for finite systems, a size-dependent diffusive to ballistic crossover can be identified [18].…”

Role of Topology in Relaxation of One-dimensional Stochastic Processes

“…The dynamics of a Markov jump process is described by the master equation, which can be regarded as a non-Hermitian Schrödinger equation because of its linearity. In recent years, there have been studies that apply topological methods to the master equations [31][32][33][34][35][36][37]. These attempts have argued localized steady states [33] and Halleffect-like chiral edge modes [35], as analogues of conventional topological edge modes.…”