Exploring Quantized Entropy Production Strength in Mesoscopic Irreversible Thermodynamics

This letter aims to investigate thermodynamic processes in small systems in the Onsager region by showing that fundamental quantities such as total entropy production can be discretized on the mesoscopic scale. Even thermodynamic variables can conjugate to thermodynamic forces, and thus, Glansdorff–Prigogine’s dissipative variable may be discretized. The canonical commutation rules (CCRs) valid at the mesoscopic scale are postulated, and the measurement process consists of determining the eigenvalues of the operators associated with the thermodynamic quantities. The nature of the quantized quantity <inline-formula> <mml:math id="mm1"> <mml:semantics> <mml:mi>β</mml:mi> </mml:semantics> </mml:math> </inline-formula>, entering the CCRs, is investigated by a heuristic model for nano-gas and analyzed through the tools of classical statistical physics. We conclude that according to our model, the constant <inline-formula> <mml:math id="mm2"> <mml:semantics> <mml:mi>β</mml:mi> </mml:semantics> </mml:math> </inline-formula> does not appear to be a new fundamental constant but corresponds to the minimum value.