Nonequilibrium fluctuations for linear diffusion dynamics

We present the theoretical study on nonequilibrium (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 nonidentical and correlated multidimensional 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(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(W). We find an interesting dynamic phase transition in the exponential tail shape of P(W), associated with a singularity found in solutions of the nonlinear differential equation. Finally, we discuss possible realizations in experiments.