# Tag Info

3

So my question is, "Why should the change in entropy be zero, even if the particles are distinguishable?" In statistical physics, entropy can be defined in many different ways. One possibility is to define it as log of the accessible phase space, given the macroscopic constraints (volume). Such entropy is not a homogeneous function of energy, volume ...

2

Under a Wick rotation, which is what you do in order to go from Minkowski to Euclidean space, both the partial derivative $\partial_0$ with respect to time and the zero-component of the gauge field transform as $$\partial_0\rightarrow i\partial_\tau$$ $$A_0\rightarrow iA_0.$$ This defines the covariant derivative for statistical field theory.

1

So lets start with the low energy configuration. To have the lowest energy all molecules must be lying in the x-y plane. Each one has 2 directions it could be lying in (x or y), and there are $N$ particles, hence $2^N$ possible configurations. (I always find picturing this with small number of molecules, say 2 or 3, for which counting the states is easy, ...

1

Addressing parts of the question out of order: ...the heat capacity would smoothly approach zero around the transition. I have never seen anyone refer to these types of transition... The heat capacity of all substances smoothly approaches zero at absolute zero. $S(E)$ has a segment of zero first derivative no, the first derivative is a constant, ...

1

I am going to address the question as to why energy and information have time symmetric conservation properties whereas entropy does not. According to the Wikipedia entry on entropy - "The entropy of an isolated system never decreases, because isolated systems spontaneously evolve towards thermodynamic equilibrium, which is the state of maximum entropy." ...

Only top voted, non community-wiki answers of a minimum length are eligible