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Fidelity mechanics is formalized as a framework to investigate quantumcritical phenomena in quantum many-body systems. This is achieved byintroducing fidelity temperature to properly quantify quantum fluctuations,which, together with fidelity entropy and fidelity internal energy, constitutethree basic state functions in fidelity mechanics, thus enabling us toformulate analogues of the four thermodynamic laws and Landauer's principle atzero temperature. Fidelity flows are defined and may be interpreted as analternative form of renormalization group flows. Thus, both stable and unstablefixed points are characterized in terms of fidelity temperature and fidelityentropy: divergent fidelity temperature for unstable fixed points and zerofidelity temperature and (locally) maximal fidelity entropy for stable fixedpoints. 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 theconstraints on a fidelity mechanical system, thus shaping fidelity flows froman unstable fixed point to a stable fixed point.  A detailed analysis of fidelity mechanical state functions is presented forthe quantum XY model, the transverse field quantum Ising chain in alongitudinal field, the spin-$1/2$ XYZ model and the XXZ model in a magneticfield.

Fidelity mechanics: analogues of the four thermodynamic laws and Landauer's principle