not because the probability of that is zero, but because it's so unlikely that it's a statistical impossibility for all practical considerations (see Crooks fluctuation theorem). Stochastic processes A stochastic process is time-reversible if the joint probabilities of the forward and reverse state sequences are the same for all sets of time increments { τs }, for s = 1, ..., k for any k: A univariate stationary Gaussian process is time-reversible. Markov processes can only be reversible if their stationary distributions have the property of detailed balance: Kolmogorov's criterion defines the condition for a Markov chain or continuous-time Markov chain to be time-reversible. Time reversal of numerous classes of stochastic processes has been studied, including Lévy processes, stochastic networks (Kelly's lemma), birth and death processes, Markov chains, and piecewise deterministic Markov processes. Waves and optics Time reversal method works based on the linear reciprocity of the wave equation, which states that the time reversed solution of a wave equation is also a solution to the wave equation since standard wave equations only contain even derivatives of the unknown variables. Thus, the wave equation is symmetrical under time reversal, so the time reversal of any valid solution is also a solution. This means that a wave's path through space is valid when travelled in either direction. Time reversal signal processing is a process in which this property is used to reverse a received signal; this signal is then re-emitted and a temporal compression occurs, resulting in a reversal of the initial excitation waveform being played at the initial source. See also T-symmetry Memorylessness Markov property Reversible computing Notes References Isham, V. (1991) "Modelling stochastic phenomena". In: Stochastic Theory and Modelling, Hinkley, DV., Reid, N., Snell, E.J. (Eds). Chapman and Hall. . Tong, H. (1990) Non-linear Time Series: A Dynamical System Approach. Oxford UP. Dynamical systems Time series Symmetry