Time-dependent fluctuation theorem

The fluctuation theorem (FT) is a generalization of the second law of thermodynamics that applies to small systems observed for short times. For thermostated systems it gives the probability ratio that entropy will be consumed rather than produced. In the present paper, we propose a version of the FT that applies to thermostated dissipative systems which respond to time-dependent dissipative fields. In testing the time-dependent fluctuation theorem we provide convincing evidence that sets of trajectories with conjugate values for the time-integrated entropy production, (+/-A+/-deltaA), are indeed (for time-reversible dynamical systems such as those studied here), time-reversal images of one another. This observation verifies the deep connection between time-reversal symmetry, the fluctuation theorem, and the second law of thermodynamics.