Non-equilibrium fluctuations for linear diffusion dynamics

Abstract

We present the theoretical study on non-equilibrium (NEQ) fluctuations for diffusion dynamics in high dimensions driven by a linear drift force. We consider a general situation in which NEQ is caused by two conditions: (i) drift force not derivable from a potential function and (ii) diffusion matrix not proportional to the unit matrix, implying non-identical and correlated multi-dimensional noise. The former is a well-known NEQ source and the latter can be realized in the presence of multiple heat reservoirs or multiple noise sources. We develop a statistical mechanical theory based on generalized thermodynamic quantities such as energy, work, and heat. The NEQ fluctuation theorems are reproduced successfully. We also find the time-dependent probability distribution function exactly as well as the NEQ work production distribution $P(\mathcal{W})$ in terms of solutions of nonlinear differential equations. In addition, we compute low-order cumulants of the NEQ work production explicitly. In two dimensions, we carry out numerical simulations to check out our analytic results and also to get $P(\mathcal{W})$. We find an interesting dynamic phase transition in the exponential tail shape of $P(\mathcal{W})$, associated with a singularity found in solutions of the nonlinear differential equation. Finally, we discuss possible realizations in experiments.

13 pages

References in corpus (6)

• Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. IV: Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics
• The Brownian gyrator: a minimal heat engine on the nano-scale
• An expression for stationary distribution in nonequilibrium steady state
• Onsager-Machlup theory for nonequilibrium steady states and fluctuation theorems
• Entropy Production of Brownian Macromolecules with Inertia
• On the work distribution for the adiabatic compression of a dilute classical gas

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