Continuity Equation - Thermodynamics

Thermodynamics

Conservation of energy (which, in non-relativistic situations, can only be transferred, and not created or destroyed) leads to a continuity equation, an alternative mathematical statement of energy conservation to the thermodynamic laws.

Letting

• u = local energy density (energy per unit volume),
• q = energy flux (transfer of energy per unit cross-sectional area per unit time) as a vector,

the continuity equation is:

Baryon number conservation is more fundamental than the first and second laws of thermodynamics. If

• n is the total number density of baryons in the local rest frame of a fluid (positive value for baryons, negative for antibaryons),
• Uα is the 4-velocity field of the baryon fluid flow,

then the 4-baryon number flux vector is Sα = nUα, satisfying the continuity equation:

This equation is true in flat or curved spacetime.