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We consider several Hamiltonian systems perturbed by external agents, thatpreserve their Hamiltonian structure. We investigate the corrections to thecanonical statistics resulting from coupling such systems with possibly largebut finite reservoirs, and from the onset of processes breaking the timereversal symmetry. We analyze exactly solvable oscillators systems, and performsimulations of relatively more complex ones. This indicates that the standardstatistical mechanical formalism needs to be adjusted, in the ever moreinvestigated nano-scale science and technology. In particular, the hypothesisthat heat reservoirs be considered infinite and be described by the classicalensembles is found to be critical when exponential quantities are considered,since the large size limit may not coincide with the infinite size canonicalresult. Furthermore, process-dependent emergent irreversibility affectsensemble averages, effectively frustrating, on a statistical level, the timereversal invariance of Hamiltonian dynamics, that is used to obtain numerousresults.

Finite reservoirs and irreversibility corrections to Hamiltonian systems statistics