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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.
T-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal, T : t ↦ − t . {\displaystyle T:t\mapsto -t.} 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 ...
Equations of mechanics are reversible in time, hence, the reverse collisions obey the same laws. This reversibility of collisions is the first example of microreversibility. According to Boltzmann, this microreversibility implies the principle of detailed balance for collisions: at the equilibrium ensemble each collision is equilibrated by its ...
Some progress can be made by studying discrete-time models or difference equations. Many discrete-time models, such as the iterated functions considered in popular fractal-drawing programs, are explicitly not time-reversible, as any given point "in the present" may have several different "pasts" associated with it: indeed, the set of all pasts ...
A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary distribution π that satisfies the detailed balance equations [13] =, where P ij is the Markov transition probability from state i to state j, i.e. P ij = P(X t = j | X t − 1 = i), and π i and π j are the equilibrium probabilities of being in states i and j, respectively ...
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.
Quantum time reversal seemed impossible due to the Second Law of Thermodynamics, but scientists finally fit the classic square peg into the quantum round hole.
Generalised time reversible (GTR) is the most general neutral, independent, finite-sites, time-reversible model possible. It was first described in a general form by Simon Tavaré in 1986. [1] The GTR model is often called the general time reversible model in publications; [2] it has also been called the REV model. [3]