text: The reversible work is the maximal useful work which can be obtained, , and can only be fully utilized in an ideal reversible process. An irreversible process produces some work , which is less than . The lost work is then ; in other words,  is the work which was lost or not exploited during the process due to irreversibilities. In terms of lost work, the theorem generally stateswhere  is the rate at which work is lost, and  is the rate at which entropy is generated. Time derivatives are denoted by dots. The theorem, as stated above, holds only for the entire thermodynamic universe - the system along with its surroundings, together:where the index "tot" denotes the total quantities produced within or by the entire universe.
  Note that  is a relative quantity, in that it is measured in relation to a specific thermal reservoir. In the above equations,  is defined in reference to the environment reservoir, at . When comparing the actual process to an ideal, reversible process between the same endpoints (in order to evaluate , so as to find the value of ), only the heat interaction with the reference reservoir  is allowed to vary. The heat interactions between the system and other reservoirs are kept the same. So, if a different reference reservoir  is chosen, the theorem would read , where this time  is in relation to , and in the corresponding reversible process, only the heat interaction with  is different. 
  By integrating over the lifetime of the process, the theorem can also be expressed in terms of final quantities, rather than rates: .