Time-Reversal and Entropy

By Christian Maes, Karel Netocny. 2002

255 citations recorded by the source corpus.

There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time-reversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations between entropy production, phase-space contraction and time-reversal starting from a deterministic dynamics. Both closed and open systems, in the transient and in the steady regime, are considered. The main result identifies under general conditions the statistical mechanical entropy production as the source term of time-reversal breaking in the path space measure for the evolution of reduced variables. This provides a general algorithm for computing the entropy production and to understand in a unified way a number of useful (in)equalities. We also discuss the Markov approximation. Important are a number of old theoretical ideas for connecting the microscopic dynamics with thermodynamic behavior.

Subfields: Physical and Theoretical Chemistry, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/42c12202a2147a70bca9c0e05dfee786adca7648

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Citations in the corpus

Stochastic thermodynamics, fluctuation theorems and molecular machines (2012, background): “Fourth, Maes emphasized that entropy production in the medium is related to that part of the stochastic action, which determines the weight of trajectories that is odd under time-reversal [17, 18].”
On the (Boltzmann) entropy of non-equilibrium systems (2003, background): “= E − ∫ K(x)dx. (30) We now observe that S(c)(n,Φtot.) must agree with the configurational entropy of a system with a Hamiltonian H ′ = m 2 ∑ v2i + ∑ φ(ri − rj) + ∑ u(ri) (31) in equilibrium at energy E′, when we choose E′ and u(x) in such a way that the equilibrium density is equal to n(x) and the…”
The large deviation approach to statistical mechanics (2008, background): “The first is that Rτ (w) provides a measure of how ‘‘out of equilibrium’’ a system is, since it yields information about the positive–negative asymmetry of nonequilibrium fluctuations that arises in general because of the irreversibility of the fluctuations paths [174,175].”
On the Entropy Production of Time Series with Unidirectional Linearity (2009, methodology): “the past on the future yields a better model [9, 8]. In the context of non-equilibrium thermodynamics it has been shown for various physical models (e.g. [10, 11], and also in a more abstract setting [12]) that statistical asymmetries between past and future can be related to thermodynamic entropy p”
Frenesy: Time-symmetric dynamical activity in nonequilibria (2019, background): “For example, the relative entropy per unit time between a steady process and its time-reversal then exactly equals the mean entropy production rate, [6, 7, 9].”
An update on the nonequilibrium linear response (2012, background): “When the perturbation is from a potential −hs V (xs), it is well established that the time-antisymmetric S(ω) = S1(ω) must be the pathdependent entropy flux into the environment as caused by the perturbation potential V [57, 58].”
Fluctuation Relations for Diffusion Processes (2007, unknown): “m µ0 so that µT = µ0P0,T . In this case, the relative entropy S(M|M˜′) may be interpreted as the entropy production in the forward process between times 0 and T, relative to the backward process, see [27, 65, 39]. Let for a measure ν(dx) = ρ(x)dx, S(ν) = − R lnρ(x)ν(dx) denotes its entropy. Using th”