Microscopic reversibility and heat for thermostatted systems

In order to test the universality of a symmetry for the trajectory obtained for Hamiltonian dynamics, we investigate the case of Nose-Hoover thermostatted dynamics with the use of a clear separation between the system and reservoir. Remarkably, the same symmetry as the Hamiltonian dynamics holds despite the presence of the dissipation, which causes the phase volume contraction. As a nontrivial application of the symmetry, we further show that the microscopic reversibility for open systems holds just as in the Hamiltonian dynamics. This bridges the first and second laws of thermodynamics under the proper definition of the work and heat.