In a physical equilibrium the system is in a state of least action – or minimum free energy – if that system is conservative – that is it obeys the laws of conservation of energy. The laws of dynamics and conservation of energy can all be deduced from the principle of least action for conservative systems.
Even in a situation of no growth – simple reproduction- without accumulation an economic equilibrium is is not like a physical equilibrium – it is a dissipative system – it requires a constant input of energy to maintain production, reproduce the workforce and maintain the capital stock against the wear and tear accounted for in depreciation. Indeed value creation – work – can be seen as the continual struggle to restore and expand the scale of a dissipative system to a larger conservative one.
This I think is why those attempts to apply the universality of the principle of least action to Economics – such as in the Samuelson – Solow growth model – have been less than successful.
There are conservation laws in economics but they are of a different kind and it is a great mistake to apply too strictly analogies with energy conservation or imply a similar conservation of money doctrine (for example Godley).
For example the principle of least action is simply energy=potential energy+kinetic energy.
The equivalent in economics would be assets=liabilities+capital. But assets here is not energy, the maintenance of the asset stock implies the continual input of energy. A non conservative system.
There is no universally accepted formulation of the extension of the principal of least action to thermodynamic and dissipative systems, which is not to state it cant be done. You can derive the laws of thermodynamics from the principle of least action but with the introduction of external energy sinks and sumps you cannot predict the course of action of the system from internal energy states alone. Feedback in dissipative systems does not have to be positive – the la Chatelier principle that Samuleson used in Foundations.
Another key difference is whether an economy is on an equilibrium or non-equilibrium path is whether expectation have been dissapointed. It takes little energy to form an expectation and no difference in energy between a correct and false expectation. However a correct expectation can be modelled as information, and an incorrect one as no information. Therefore equilibrium can be modelled as a state of maximum entropy – which is equivalent of least action. This value creation system though is parallel and separate from – though connected to – the system for valuation of past work. It is the creation of value which links the two.
One issue over which there is great confusion is whether economic systems – being inter-temporal and dynamic – are different from economic systems where prices shift according to the compatibility of plans and expectations. If plans are compatible so that expectations are realized then an external disequilibrium input will cause a ‘shock’ – there will be a price path but that path will restore to equilibrium. This is an example of Wicksells ‘Rocking Horse’ – which requires a Frisch’s type ‘shock’ of a hammer hitting it to knock out of equilibrium. This is why the term ‘inter-temporal equilibrium’ is a misnomer. There is no such thing – rather it is the path of reaction of a conservative system towards equilibrium. Equilibrium is not a law – rather it is a result of a law – the principle of least action – that describes the state of a system fully at all points along its path in and out of equilibrium.
If however plans are incompatible and expectations are not realised then negative feedback is introduced – we have a dissipative system – value will be net created or destroyed. Most plans are incompatible most of the time. The creation and destruction will create net winners and losers. There will be opportunities for arbitrage and bringing plans back into compatibility. The act of economic failure and mispricing destroys value but creates information. So far as these opportunities are not realised then the negative feedback will continue. The economic system will drift away from the point of maximum information. Expected prices will become more and more misvalued. Only when these expectations change and the price system increases in information content will an equilibrium path be restored. The introduction of feedbacks makes the system non-linear. The ‘normal’ state of the system need not be at rest – it can be a limit cycle – with saddlepoint properties outside a certain range. This is another reason why it is better to think in terms of the underyling causative forces of least action and maximisation of information rather than the fixed point of equilibrium at rest.
This approach also has applications in terms of thinking about money. If expectations are held for all time and are correctly realised then- as Hahn set down – money has no function. However if the value of products is uncertain then a mechanism is needed to guarantee the realisation of a contract in the future. Money as a store of value is an information store allowing the alignment of two plans in the future.