  The entropy shows an unavoidable tendency of disorder in thermostatistics
according to the second thermodynamics law. This provides a minimization
entropy principle for quantum thermostatistics with the von Neumann entropy and
nonextensive quantum thermostatistics with special Tsallis entropy. Our goal in
this work is to provide operational characterizations of general entropy
measures. We present the first unified principle consistent with the second
thermodynamics law in terms of general quantum entropies for both quantum
thermostatistics and nonextensive quantum thermostatistics. This further
reveals new features beyond the second thermodynamics law by maximization the
cross entropy during irreversible measurement procedures. The present result is
useful for asymptotical tasks of quantum entropy estimations and universal
quantum source encoding without the state tomography. It is further applied to
single-shot state transitions and cooling in quantum thermodynamics with
limited information. These results should be interesting in the many-body
theory and long-range quantum information processing.
