Uncertainty Relations in Thermodynamics of Irreversible Processes on a Mesoscopic Scale

Abstract: Studies of mesoscopic structures have now become a leading and rapidly evolving research field ranging from physics, chemistry, and mineralogy to life sciences. The increasing miniaturization of devices with length scales of a few nanometers is leading to radical changes not only in the realization of new materials but also in shedding light on our understanding of the fundamental laws of nature that govern the dynamics of systems at the mesoscopic scale. On the basis of recent experimental results and previous theoretical research, we investigate thermodynamic processes in small systems in Onsager's region. We show that fundamental quantities such as the total entropy production, the thermodynamic variables conjugate to the thermodynamic forces, and the Glansdorff-Prigogine's dissipative variable may be discretized at the mesoscopic scale. We establish the canonical commutation rules (ccr) valid at the mesoscopic scale. The numerical value of the discretization constant is estimated experimentally. The ultraviolet divergence problem is solved by applying the correspondence principle with Einstein-Prigogine's fluctuations theory in the limit of macroscopic sy