  Fidelity mechanics is formalized as a framework to investigate quantum
critical phenomena in quantum many-body systems. This is achieved by
introducing fidelity temperature to properly quantify quantum fluctuations,
which, together with fidelity entropy and fidelity internal energy, constitute
three basic state functions in fidelity mechanics, thus enabling us to
formulate analogues of the four thermodynamic laws and Landauer's principle at
zero temperature. Fidelity flows are defined and may be interpreted as an
alternative form of renormalization group flows. Thus, both stable and unstable
fixed points are characterized in terms of fidelity temperature and fidelity
entropy: divergent fidelity temperature for unstable fixed points and zero
fidelity temperature and (locally) maximal fidelity entropy for stable fixed
points. In addition, an inherently fundamental role of duality is clarified,
resulting in a canonical form of the Hamiltonian in fidelity mechanics.
Dualities, together with symmetry groups and factorizing fields, impose the
constraints on a fidelity mechanical system, thus shaping fidelity flows from
an unstable fixed point to a stable fixed point.
  A detailed analysis of fidelity mechanical state functions is presented for
the quantum XY model, the transverse field quantum Ising chain in a
longitudinal field, the spin-$1/2$ XYZ model and the XXZ model in a magnetic
field.
