Before revision:  This problem arises in various scenarios in thermodynamics of computation and nonequilibrium statistical physics  (e.g., when designing processes to implement some desired computation, feedback-control protocol, or Maxwellian demon).
After revision:  This problem arises often in the thermodynamics of computation and nonequilibrium statistical physics (e.g., when designing processes to implement some desired computation, feedback-control protocol, or Maxwellian demon).