# What is pressure at microscopic level in a liquid? how can I imagine it? [duplicate]

what i mean to say is that, in a liquid (ideal) pressure gets transmitted undiminished, what it means is that a molecule applies equal amount of force to all the molecules in its vicinity how? how do non ideal liquids not satisfy this condition.

• The question is not very clear but I can tell you right away that pressure is a macroscopic emergent property that has little meaning in the microscopic realm, just like entropy and other quantities we are used to. – Swike Nov 30 '19 at 10:57
• @Swike Are you sure entropy "has little meaning in the microscopic realm"? The Boltzmann definition states entropy is a measure of the number of microscopic states in thermodynamic equilibrium, consistent with its macroscopic thermodynamic properties (or macrostate). – Bob D Nov 30 '19 at 15:34
• @BobD I think this is correct. In fact it is Boltmann's definition that brought this idea into place. If you look to very very simple systems (by simple we understand a system that is made of few operating elements), which tends to be the norm for microscopic physical systems, you either have very little information to construct a macroscopic variable at all, or you have a situation where the number of microstates for each macroscopic quantity is extremely low and the distribution is so flattened that you can expect fluctuations getting so large that the second law is no longer meaningfull. – Swike Nov 30 '19 at 22:21

A possible microscopic observable is the so called microscopic stress tensor. For a system of particles in a volume $$V$$ interacting through pair-wise forces $${\bf f}_{ij}$$ it is $${\bf \sigma} = \frac{1}{V}\sum_i \left[ -m_i {\bf \dot u}_i\otimes{\bf \dot u}_i + \frac{1}{2}\sum_{j\neq i} {\bf r}_{ij}\otimes{\bf f}_{ij}\right]$$ where $${\bf u}_i$$ is the velocity of the $$i$$-th particle referred to the average velocity and $${\bf r}_{ij}= {\bf r}_{i}-{\bf r}_{j}$$.
At equilibrium, the average of each diagonal component $${\bf \sigma}_{\alpha \alpha}$$ is equal to the others and it is also equal to thermodynamic pressure.