We investigate the loss of adiabaticity when cooling a many-body quantum
system from an initial thermal state towards a quantum critical point. The
excitation density, which quantifies the degree of adiabaticity of the
dynamics, is found to obey scaling laws in the cooling velocity as well as in
the initial and final temperatures of the cooling protocol. The scaling laws
are universal, governed by the critical exponents of the quantum phase
transition. The validity of these statements is shown analytically for a Kitaev
quantum wire coupled to Markovian baths, and subsequently argued to be valid
under rather general conditions. Our results establish that quantum critical
properties can be probed dynamically at finite temperature, without even
varying the control parameter of the quantum phase transitions.Comment: 5+4 pages, 2+2 figures; companion paper to "Long-range Kitaev chain
in a thermal bath: Analytic techniques for time-dependent systems and
environments" by the same authors and submitted on the same da