In the systems sciences system equivalence is the behavior of a parameter or component of a system in a way similar to a parameter or component of a different system. Similarity means that mathematically the parameters and components will be indistinguishable from each other. Equivalence can be very useful in understanding how complex systems work. Overview Examples of equivalent systems are first- and second-order (in the independent variable) translational, electrical, torsional, fluidic, and caloric systems. Equivalent systems can be used to change large and expensive mechanical, thermal, and fluid systems into a simple, cheaper electrical system. Then the electrical system can be analyzed to validate that the system dynamics will work as designed. This is a preliminary inexpensive way for engineers to test that their complex system performs the way they are expecting. This testing is necessary when designing new complex systems that have many components. Businesses do not want to spend millions of dollars on a system that does not perform the way that they were expecting. Using the equivalent system technique, engineers can verify and prove to the business that the system will work. This lowers the risk factor that the business is taking on the project. The following is a chart of equivalent variables for the different types of systems {| class="wikitable" |- ! System type ! Flow variable ! Effort variable ! Compliance ! Inductance ! Resistance |- | Mechanical | dx/dt | F = force | spring (k) | mass (m) | damper (c) |- | Electrical | i = current | V = voltage | capacitance (C) | inductance (L) | resistance (R) |- | Thermal | qh = heat flow rate | ∆T = change in temperature | object (C) | inductance (L) | conduction and convection (R) |- | Fluid | qm = mass flow rate, qv = volume flow rate | p = pressure, h = height | tank (C) | mass (m) | valve or orifice (R) |} Flow variable: moves through the system Effort variable: puts the system into action Compliance: stores energy as potential Inductance: stores energy as kinetic Resistance: dissipates or uses energy The equivalents shown in the chart are not the only way to form mathematical analogies. In fact there are any number of ways to do this. A common requirement for analysis is that the analogy correctly models energy storage and flow across energy domains.