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Fluctuations and correlations in nonequilibrium systems

Nonequilibrium systems exchange the energy with an environment in the form of work and heat. The work done on a system obeys the fluctuation theorem, while the dissipated heat which differs from the work by the internal energy change does not. We derive the modified fluctuation relation for the heat in the overdamped Langevin system. It shows that mutual correlations among the work, the heat, and the internal energy change are responsible for the different fluctuation property of the work and the heat. The mutual correlation is investigated in detail in a two-dimensional linear diffusion system. We develop an analytic method which allows one to calculate the large deviation function for the joint probability distributions. We find that the heat and the internal energy change have a negative correlation, which explains the reason for the breakdown of the fluctuation theorem for the heat.