Thanks! Also, if a map is differentiable, it is also continuous and so the proof can be made really simple, right?
BTW, could you explain to me how to type latex code?
How can the conservation of energy be applied to the entire universe? How can we define the energy of the universe? Is this definition unique for different observers? What is the difference between the thermodynamics universe (system+environment) and the cosmological universe?
@ZapperZ: thank you for the very informative articles (I really enjoyed reading them). Could you perhaps clarify some points?
1. If I am getting it right, entropy decreases because of day/night temperature differences and this decrease is much greater than the decrease in entropy due to life...
How do life and all processes linked to life go along with the second law of thermodynamics? If living creatures decrease their entropy because they are open systems and in a state of non-equilibrium with the environment, in general does the total entropy increase? (for example, if we have two...
I would like someone to explain to me the correlations between these thermodynamics concepts:
1 State function/conservative force/reversibility
2 State function/exact differential
Some functions in the phase space of a system are state function some are not. Is this simply an empirical...
Also, primordial black holes, formed in the early stage of the history of the universe, might exist. Primordial black holes are not the result of the gravitational collapse of a pre-existing massive star, but were mainly created in the extreme conditions after the Big Bang. They might be of any...