  We investigate the fine-grained uncertainty relations for qubit system by
measurements corresponding respectively to two and three spin operators. Then
we derive the general bound for a combination of two probabilities of
projective measurements in mutually unbiased bases in $d$-dimensional Hilbert
space. All of those uncertainty inequalities can be applied to construct
different thermodynamic cycles such that the violation of those inequalities
will lead to the violation of the second law of thermodynamics. This reveals
the relationship between fine-grained uncertainty and the second law of
thermodynamics.
