Continuum mechanics versus violations of the second law of thermodynamics

Spontaneous, random violations of the second law become relevant as the length and/or timescales become very small. Modern statistical physics tells us that the second law then needs to be replaced by the fluctuation theorem and, mathematically, the irreversible entropy evolves as a submartingale. This is illustrated on the Couette flow of a molecular fluid. On the continuum level, such phenomena lead to a framework of thermomechanics relying on stochastic (rather than deterministic) functionals of energy and entropy, which are applied in heat diffusion and thermoelasticity settings. Counterintuitive thermomechanical behaviors are also discussed in (1) the evolution of acceleration wavefronts of nanoscale thickness and (2) the fluid mechanics which has to enter a permeability model of a poroelastic medium with nanoscale pores.