We theoretically show that strongly forbidden oscillations of a specific heat have to exist in metallic phases of some quasi-one-dimensional (Q1D) conductors. They appear due to electron-electron interactions under the condition of the magnetic breakdown phenomenon between the so-called open interference electron orbits. We argue that such forbidden thermodynamic oscillations can exist in Q1D conductors (TMTSF)${}_2{\mathrm{ClO}}_4$ and (Per)${}_2\mathrm{Au}$(mnt)${}_2$, where TMTSF stands for tetramethyltetraselenafulvalene, Per is polycyclic aromatic hydrocarbon, and mnt is mononitrotoluene, and we suggest how to discover them.

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• Fermi surface
• High magnetic fields
• Landau theory
• Quantum interference effects
• Specific heat