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Covers the study of (primarily homogeneous) macroscopic systems from a heat/energy/entropy point of view. Consider also using the tag: [statistical-mechanics].

1 vote
0 answers
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Canonical Ensemble/Measure maximises differential entropy

Denote the so-called canonical ensemble as $\mu$ : $$ \mu(dq,dp)=Z^{-1}_\beta e^{-\beta H(q,p)}dqdp. $$ (with say $p,q \in \mathbb{R}^{3N}$ for some $N\in \mathbb{N}$ and $Z_\beta$ the normalisation c …
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0 votes
1 answer
102 views

Difference Between Molecular Dynamics and Kinetic Theory? Loschmidt's

I have heard Loschmidt's paradox described as "the laws of thermodynamics are time asymmetric because entropy always increases, but the underlying laws of physics are symmetric under time reversal." … Could someone explain the main difference between thermodynamics (is this the same as Kinetic Theory or Statistical Mechanics?) …
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7 votes
4 answers
2k views

In the Langevin dynamics: neglecting inertia. A mathematician trying to understand physics t...

If we write the Langevin equation: for a particle with mass $m$, position $x$ and velocity $v$, with some damping coefficient $\gamma$, $$ m dV(t)=-\gamma V(t)dt+dW(t) ,~~~~~~~dX(t)=V(t)dt.$$ Then as …
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