Where does dissipation collide?

William Thomson (Lord Kelvin) named this meaning in his 1852 paper On a universal tendency in nature to the dissipation of mechanical energy, which argued that natural processes tend to turn usable mechanical energy into heat that can no longer be fully recovered as work. In later thermodynamics this became the idea that irreversible processes, such as friction or unrestrained heat flow, produce entropy and leave less energy available to do work. The referent here is a physical change in a real system, where ordered energy degrades into disordered heat. It is not resources burned in an economic contest, a mathematical property of a control system, or money squandered in a divorce.[1]

Unit

A quantity of mechanical or free energy converted to heat, in joules

Recovery means

None: the process is irreversible, so the degraded energy is not recoverable as work

Measured by

Quantified through entropy production or lost available work, in joules per kelvin or in joules

Gordon Tullock introduced this meaning in his 1967 paper The welfare costs of tariffs, monopolies, and theft, showing that when people compete to capture a monopoly or a government-granted advantage, the resources they spend on that competition are a social loss. Richard Posner's 1975 The social costs of monopoly and regulation sharpened the point by arguing that, under competition for the prize, the whole value of the monopoly rent can be used up in the effort to win it. The referent is wasted real resources, such as lobbying and effort, spent chasing a transfer rather than creating value. It is not energy turning to heat, an input-output property of a system, or the wasting of a couple's shared assets.[2][3]

Unit

The value of resources spent competing for a rent, in currency

Recovery means

Not applicable

Measured by

Estimated as the resources expended in the contest relative to the value of the prize

Jan Willems introduced this meaning in his 1972 paper Dissipative dynamical systems part I: General theory, which defined a system as dissipative when the energy it stores can never rise above the energy supplied to it from outside. The property is made precise by a storage function that tracks internal energy and a supply rate that tracks what flows in, with the storage never exceeding the accumulated supply. The referent is an abstract property of a dynamical system, defined by an energy-like balance and used to analyze stability, rather than a specific physical process. It differs from the physical degradation of energy to heat, resources wasted in an economic contest, and marital property squandered in a divorce.[4]

Unit

A property of a dynamical system, defined by a supply rate and a storage function

Recovery means

Not applicable

Measured by

Verified by finding a nonnegative storage function whose increase never exceeds the supplied energy

In United States divorce law, dissipation refers to one spouse's use of marital property for a purpose unrelated to the marriage, for that spouse's sole benefit, at a time when the marriage is breaking down. The Illinois Supreme Court stated this standard in In re Marriage of O'Neill (1990), and Sarah Acker's 2006 article All's fair in love and divorce reviewed how courts apply it when dividing property. The referent is squandered or hidden household wealth, which a court can charge back against the offending spouse's share of the estate. It is not energy lost as heat, resources spent chasing a monopoly, or a stability property of a control system.[7][5][6]

Unit

An amount of marital property spent for one spouse's sole benefit, in currency

Recovery means

The court may charge the dissipated amount back against the spending spouse's share

Measured by

Established in court by tracing expenditures made after the marriage began breaking down