Independence of the transient fluctuation theorem to thermostatting details.

The fluctuation theorems show how macroscopic irreversibility arises from time reversible microscopic dynamics. They have been confirmed in computer simulations and in laboratory experiments. The standard proofs of the transient fluctuation theorems involve the use of time reversible deterministic thermostats to control the temperature of the system of interest. These mathematical thermostats do not occur in Nature. However, since in a gedanken experiment the thermostatting regions can be removed arbitrarily far from the system of interest, it has been argued that the precise details of the thermostat cannot be important and that the resulting fluctuation theorems apply to natural systems. In this paper we give a detailed analysis showing how the fluctuation theorem is independent of the precise mathematical details of the thermostatting mechanism for an infinite class of fictitious time reversible deterministic thermostats. Our analysis reinforces the implications of the gedanken experiment and implies that thermostats used in the derivations of fluctuation theorems are a convenient but ultimately irrelevant device.