Nonreversibility

Nonreversibility, or irreversibility, is the property of a process or system that cannot, in general, be reversed to restore its original state without external intervention. It emphasizes an asymmetry between forward and backward evolution.

In thermodynamics, irreversible processes generate entropy and move systems toward equilibrium. Real processes such as friction, viscous dissipation, turbulent mixing, heat transfer across finite temperature differences, and spontaneous chemical reactions are typically irreversible. Reversible processes are idealizations: quasi-static transformations with no entropy production, where the system can be returned to its initial state by infinitesimal changes in conditions. The distinction underpins the thermodynamic arrow of time: microscopic laws may be time-symmetric, but macroscopic evolution tends to be irreversible because many microstates correspond to a single macrostate, and entropy tends to increase.

In mathematics and dynamical systems, noninvertibility means that a system’s future state does not uniquely determine its past. A noninvertible map can collapse distinct states into the same image, so information about earlier conditions is lost. For example, the function f(x)=x^2 maps x and −x to the same value.

In information theory and computing, nonreversibility describes transformations that are easy to compute but hard to invert. Cryptographic hash functions and irreversible data compression illustrate this property. In physics and engineering, irreversibility accounts for inefficiencies and limits on energy conversion.

Common examples include mixing of substances, dissipative heat flow, plastic deformation, and spontaneous chemical reactions.