Energy can be built from lagrangian when considering the symmetry of time $(\frac{\partial L}{\partial t}=0)$. Free energy is a generalization of energy when the system exchanges heat with the environment. I can't find any sources that building free energy directly from lagrangian. Is there any way to do that? If it is, what symmetry is it based on?

Free energy is a generalization of energy when the system exchanges heat with the environment. Energy, in its turn, can be extracted from lagrangian under the symmetry of time $(\frac{\partial L}{\partial t}=0)$. However, I can't find any sources that links the free energy directly from lagrangian. Is there any way to do that? If it is, what symmetry is it based on?

Energy can be built from Lagrangian when considering the symmetry of time $(\frac{\partial L}{\partial t}=0)$. Free energy is a generalization of energy when the system exchanges heat with the environment. I can't find any sources that building free energy directly from Lagrangian. Is there any way to do that? If it is, what symmetry is it based on?

Energy can be built from lagrangian when considering the symmetry of time $(\frac{\partial L}{\partial t}=0)$. Free energy is a generalization of energy when the system exchanges heat with the environment. I can't find any sources that building free energy directly from lagrangian. Is there any way to do that? If it is, what symmetry is it based on?