# What is the definition of the Potential of Mean Force (PMF) in physics jargon?

What's the common term for PMF in statistical physics?

Is it plausible to use the chemists' PMF even in non-equilibrium systems that don't follow the canonical ensemble rules or Maxwell-Boltzmann distribution?

Is writing the following valid?

$$\mathcal{P}(x) = \frac{\int d\mathbf{q} \, \delta[x-x(\mathbf{q})] \exp(-E(\mathbf{q})/k_BT)}{\int d\mathbf{q} \, \exp(-E(\mathbf{q})/k_BT)} \equiv \frac{\mathcal{Q}(x)}{Q}$$

Where $$\mathcal{Q}(x)$$ is the partition function.

Finally, the expression for the probability density $$\mathcal{P}(x)$$ is perfectly valid. Its intuitive meaning is to sum the probability of all the states such that the function $$x({\bf q})$$ is equal to $$x$$.
• What about calling it the $-KT log$ of some histogram over an order parameter as a generalized free energy? – 0x90 Apr 13 at 15:52
• Can't we use $e^ { -\Delta F / k T} = \overline{ e^{ -W/kT } }$ some how to justify this: $Q(x=x')∝exp⁡^{(-A(x = x' )/(K_B T))}$ where $A$ is "free energy"? – 0x90 May 15 at 22:00