[chunky1994]

I'm a bit skeptical to give up conservation of energy in a system with friction. Isn't it more accurate to say that if we were to calculate every specific interaction we'd still end up having conservation of energy. Now whether or not we're dealing with a closed system etc becomes important but if we were to able to truly model the entire physical system with friction, we'd still adhere to our conservation laws.

So they are not approximations, but are just terribly difficult calculations, no?

Maybe I'm misunderstanding your point, but this should be true regardless of our philosophy of physics correct?

[nyrikki]

It is an analogy stating that dissipative systems do not have a Lagrangian, Noether's work applies to Lagrangian systems

Conservation laws in particular are measurable properties of an isolated physical system do not change as the system evolves over time.

It is important to remember that Physics is about finding useful models that make useful predictions about a system. So it is important to not confuse the map for the territory.

Gibbs free energy and Helmholtz free energy are not conserved.

As thermodynamics, entropy, and entropy are difficult topics due to didactic half-truths, here is a paper that shows that the nbody problem becomes invariant and may be undecidable due to what is a similar issue (in a contrived fashion)

http://philsci-archive.pitt.edu/13175/

While Noether's principle often allows you to see things that can often be simplified in an equation, often it allows you to not just simplify 'terribly difficult calculations' but to actually find computationally possible calculations.