Mechanical equilibrium

A thermodynamic system is in mechanical equilibrium if there is no net macroscopic force producing acceleration of any part of the system. Operationally, this means stresses balance so that there is no spontaneous bulk motion driven by pressure (or more general mechanical) imbalances.

For a simple compressible fluid, mechanical equilibrium typically implies:

• the pressure is uniform within each connected region (in the absence of body forces), and
• at a movable boundary (e.g., a frictionless piston), the internal pressure matches the external mechanical load from the surroundings .

Physical interpretation

If mechanical equilibrium fails, pressure/stress differences do work on the system’s parts, producing motion (expansion, compression, flow) until force balance is restored. Such motion is a thermodynamic process and—when accompanied by friction, viscosity, shocks, or turbulence—typically generates dissipation and thus irreversibility .

Mechanical equilibrium is one ingredient of full thermodynamic equilibrium ; the latter also requires thermal and chemical equilibration.

Key properties and relations

Boundary force balance (piston model). For a piston of area $A$ with external load force $F_{\text{load}}$ (including weights), force balance gives

so $P_{\text{in}} = P_{\text{out}} + F_{\text{load}}/A$. In the common idealization of negligible additional load, $P_{\text{in}} = P_{\text{out}}$.

Hydrostatic balance (body forces). In a static fluid under gravity, mechanical equilibrium allows a pressure gradient that balances weight:

so “no motion” does not necessarily mean “spatially constant pressure” when body forces act.

Thermodynamic conjugacy. In equilibrium thermodynamics, pressure is the intensive variable conjugate to volume . For a simple system described by internal energy $U(S,V,N)$, one relation is

linking mechanical response to derivatives of an equilibrium state function.