Fidelity Mechanics: Analogues of four thermodynamic laws and Landauer¹s principle

Fidelity mechanics, a scheme to investigate critical phenomena in quantum many-body physics, is formulated as an analogue of four laws in thermodynamics and black hole mechanics, thus unveiling a formal connection between critical points and black holes. Rich physics is unveiled even for simple, or say, prototypical models in quantum many-body systems, such as one-dimensional quantum XY model and quantum transverse Ising chain in a longitudinal field. This enables us to clarify a confusing point for the so-called long-range entanglement driven order. The latter is believed to be present in the disordered regime for quantum XY chain. Fidelity mechanics might also offer an alternative solution to other mysterious problems in physics, including its cosmological implications for the interpretation of dark matter and dark energy.