The thermodynamic influence of quantum probing on an object is studied. Here, quantum probing is understood as a pre-measurement based on a non-demolition interaction, which records some information of the probed object, but does not change its energy state when both the probing apparatus and the probed object are isolated from the environment. It is argued that when the probing apparatus and the probed object are immersed in a same equilibrium environment, the probing can affect the effective temperature of the object or induce a quantum isothermal process for the object to transfer its energy. This thermodynamic feature can be regarded as a witness of the existence of quantum probing even if the quantum probing would not disturb the object if the environment were not present.
For Hawking radiation, treated as a tunneling process, the no-hair theorem of black hole together with the law of energy conservation is utilized to postulate that the tunneling rate only depends on the external qualities (e.g., the mass for the Schwarzschild black hole) and the energy of the radiated particle. This postulate is justified by the WKB approximation for calculating the tunneling probability. Based on this postulate, a general formula for the tunneling probability is derived without referring to the concrete form of black hole metric. This formula implies an intrinsic correlation between the successive processes of the black hole radiation of two or more particles. It also suggests a kind of entropy conservation and thus resolves the puzzle of black hole information loss in some sense.
