Nonadiabatic response theory: The case of volume change

Using the field-theoretical formalism, nonequilibrium thermodynamics is discussed where the volume V(t) is changing with time. The time-dependent boundary condition on the wave function is handled by introducing the time-independent mode variables, thus leading to the time-independent Fock space. The correct representation of the second quantized Hamiltonian is derived which depends explicitly on both V(t) and V ̇ \.{}{}(t). This leads to two kinds of force operators, X₁⁰(t) (pressure) and an extra term X₂(t). The adiabatic expansion of the increase {Δ}E(t) of internal energy is performed and it is shown that X₂(t) has no effect up to the leading nonequilibrium correction. The resulting form of {Δ}E(t) ensures that the correction is positive, thus proving the principle of maximum-minimum work.