  All living cells transport molecules and ions across membranes, often against
concentration gradients. This active transport requires continual energy
expenditure and is clearly a nonequilibrium process for which standard
equilibrium thermodynamics is not rigorously applicable. Here we derive a
nonequilibrium effective potential that evaluates the per particle transport
energy invested by the membrane. A novel method is used whereby a Hamiltonian
function is constructed using particle concentrations as generalized
coordinates. The associated generalized momenta are simply related to the
individual particle energy from which we identify the effective potential.
Examples are given and the formalism is compared with the equilibrium Gibb's
free energy.
