Abstract
We discuss the physical meaning and significance of statistical forces on quasi-static probes in first order around detailed balance for driven media. Exploiting the quasi-static energetics and the structure of (McLennan) steady nonequilibrium ensembles, we find that the statistical force obtains a nonequilibrium correction deriving from the excess work of driving forces on the medium in its relaxation after probe displacement. This reformulates, within a more general context, the recent result by Nakagawa (2014 Phys. Rev. E 90 022108) on thermodynamic aspects of weakly nonequilibrium adiabatic pumping. It also proposes a possible operational tool for accessing some excess quantities in steady state thermodynamics. Furthermore, we show that the point attractors of a (macroscopic) probe coupled to a weakly driven medium realize the predictions of the minimum entropy production principle. Finally, we suggest a method to measure the relative dynamical activity through different transition channels, via the measurement of the statistical force induced by a suitable driving.
Highlights
Statistical forces are responsible in thermodynamics for generating transport of energy, momentum or matter as a result of the irreversible tendency to approach equilibrium [1]
Exploiting the quasi-static energetics and the structure of (McLennan) steady nonequilibrium ensembles, we find that the statistical force obtains a nonequilibrium correction deriving from the excess work of driving forces on the medium in its relaxation after probe displacement
That is why it can be useful to find that the statistical force on a probe is directly related to excess work, at least close to equilibrium and for thermodynamic transformations controlled by mechanical motion of a probe
Summary
Where dW ex denotes the excess thermodynamic work of the driving forces in the medium along the relaxation process that corresponds to the thermodynamic transformation x → x+dx, T → T +dT , and dQex is the (incoming) excess heat. Our observation on the absence of the first-order correction in the free energy provides a simple variation of formula (13) in [9] by Nakagawa for the work transfer during cyclic adiabatic pumping in terms of nonequilibrium (excess) heat into the driven system. Formula (4) gives a direct relation between the mechanical force on the probe on the slow time scale and the steady-state thermodynamic process in the medium on the fast time scale. We give the statistical mechanical basis for the above general thermodynamic arguments
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