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[a] While processes in isolated systems are never reversible, [3] cyclical processes can be reversible or irreversible. [4] Reversible processes are hypothetical or idealized but central to the second law of thermodynamics. [3] Melting or freezing of ice in water is an example of a realistic process that is nearly reversible.
For processes that include the transfer of matter, a further statement is needed. When two initially isolated systems are combined into a new system, then the total internal energy of the new system, U system , will be equal to the sum of the internal energies of the two initial systems, U 1 and U 2 : U s y s t e m = U 1 + U 2 . {\displaystyle ...
where a reversible path is chosen from absolute zero to the final state, so that for an isothermal reversible process Δ S = Q r e v T {\displaystyle \Delta S={Q_{rev} \over T}} . In general, for any cyclic process the state points can be connected by reversible paths, so that
The Newton and the Schrödinger equations in the absence of the macroscopic magnetic fields and in the inertial frame of reference are T-invariant: if X(t) is a solution then X(-t) is also a solution (here X is the vector of all dynamic variables, including all the coordinates of particles for the Newton equations and the wave function in the configuration space for the Schrödinger equation).
A process is said to be physically reversible if it results in no increase in physical entropy; it is isentropic. There is a style of circuit design ideally exhibiting this property that is referred to as charge recovery logic , adiabatic circuits , or adiabatic computing (see Adiabatic process ).
The reversible heat engine efficiency can be determined by analyzing a Carnot heat engine as one of reversible heat engine. This conclusion is an important result because it helps establish the Clausius theorem, which implies that the change in entropy is unique for all reversible processes: [4]
Given that a phase change is an internally reversible process, and that our system is closed, the first law of thermodynamics holds: = + =, where is the internal energy of the system.
Many redox processes observed by CV are quasi-reversible or non-reversible. In such cases the thermodynamic potential E 0 1/2 is often deduced by simulation. The irreversibility is indicated by i pa /i pc ≠ 1. Deviations from unity are attributable to a subsequent chemical reaction that is triggered by the electron transfer.