  In this paper we present a first-principles analysis of the nonequilibrium
work distribution and the free energy difference of a quantum system
interacting with a general environment (with arbitrary spectral density and for
all temperatures) based on a well-understood micro-physics (quantum Brownian
motion) model under the conditions stipulated by the Jarzynski equality [C.
Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)] and Crooks' fluctuation theorem
[G. E. Crooks, Phys. Rev. E 60, 2721 (1999)] (in short FTs). We use the
decoherent history conceptual framework to explain how the notion of
trajectories in a quantum system can be made viable and use the
environment-induced decoherence scheme to assess the strength of noise which
could provide sufficient decoherence to warrant the use of trajectories to
define work in open quantum systems. From the solutions to the Langevin
equation governing the stochastic dynamics of such systems we were able to
produce formal expressions for these quantities entering in the FTs, and from
them prove explicitly the validity of the FTs at the high temperature limit. At
low temperatures our general results would enable one to identify the range of
parameters where FTs may not hold or need be expressed differently. We explain
the relation between classical and quantum FTs and the advantage of this
micro-physics open-system approach over the phenomenological modeling and
energy-level calculations for substitute closed quantum systems.
