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A mathematical or physical process is time-reversible if the dynamics of the process remain well-defined when the sequence of time-states is reversed.. A deterministic process is time-reversible if the time-reversed process satisfies the same dynamic equations as the original process; in other words, the equations are invariant or symmetrical under a change in the sign of time.
In physics, Loschmidt's paradox (named for J.J. Loschmidt), also known as the reversibility paradox, irreversibility paradox, or Umkehreinwand (from German 'reversal objection'), [1] is the objection that it should not be possible to deduce an irreversible process from time-symmetric dynamics.
T-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal, :. Since the second law of thermodynamics states that entropy increases as time flows toward the future, in general, the macroscopic universe does not show symmetry under time reversal. In other words, time is said to be ...
In some contexts the concept of stopping time is defined by requiring only that the occurrence or non-occurrence of the event τ = t is probabilistically independent of X t + 1, X t + 2, ... but not that it is completely determined by the history of the process up to time t. That is a weaker condition than the one appearing in the paragraph ...
There are two major, closely related types of reversibility that are of particular interest for this purpose: physical reversibility and logical reversibility. [ 2 ] A process is said to be physically reversible if it results in no increase in physical entropy ; it is isentropic .
Another discrete-time process that may be derived from a continuous-time Markov chain is a δ-skeleton—the (discrete-time) Markov chain formed by observing X(t) at intervals of δ units of time. The random variables X (0), X (δ), X (2δ), ... give the sequence of states visited by the δ-skeleton.
Time-reversibility An immediate consequence of instantaneity, time-reversibility means that a time-reversed Stokes flow solves the same equations as the original Stokes flow. This property can sometimes be used (in conjunction with linearity and symmetry in the boundary conditions) to derive results about a flow without solving it fully.
When the connections are time-independent rate constants, the master equation represents a kinetic scheme, and the process is Markovian (any jumping time probability density function for state i is an exponential, with a rate equal to the value of the connection).