You can burn carbon at one location, and unburn it elsewhere. For instance, you could burn it on planes, which benefit directly from fossil fuels' high energy density, and then unburn it in areas with surplus of solar or wind power, taking energy from renewable sources.
Here, no thermodynamics violated, and yet the system allows us to eat our cake (high-density energy storage) and eat it too (net zero carbon emissions).
You can burn carbon at one location, and unburn it elsewhere. For instance, you could burn it on planes, which benefit directly from fossil fuels' high energy density, and then unburn it in areas with surplus of solar or wind power, taking energy from renewable sources.
Here, no thermodynamics violated, and yet the system allows us to eat our cake (high-density energy storage) and eat it too (net zero carbon emissions).