Abstract
We survey new extensions of continuum mechanics incorporating spontaneous violations of the Second Law (SL), which involve the viscous flow and heat conduction. First, following an account of the Fluctuation Theorem (FT) of statistical mechanics that generalizes the SL, the irreversible entropy is shown to evolve as a submartingale. Next, a stochastic thermomechanics is formulated consistent with the FT, which, according to a revision of classical axioms of continuum mechanics, must be set up on random fields. This development leads to a reformulation of thermoviscous fluids and inelastic solids. These two unconventional constitutive behaviors may jointly occur in nano-poromechanics.
Highlights
As is well known, the Second Law can be expressed in terms of a deterministic inequality (e.g., [1]) ∆S(ir) ≥ 0, (1)where ∆S(ir) is the irreversible part of the entropy increment ∆S
While random fluctuations are negligible on macroscales, the Second Law gets spontaneously violated on very small scales, as expressed by the so-called fluctuation theorem (FT) which gives the relative probability of observing processes that have positive (A) and negative (− A) total dissipation in non-equilibrium systems [2,3]: P
There are three types of classical physics phenomena where spontaneous violations occur–viscous flow [6], heat conduction [7], and electrical resistance [3]—and in this paper we review the recently introduced extensions of continuum mechanics incorporating the first two of these
Summary
The Second Law can be expressed in terms of a deterministic inequality (e.g., [1]). While random fluctuations are negligible on macroscales, the Second Law gets spontaneously violated on very small (molecular) scales, as expressed by the so-called fluctuation theorem (FT) which gives the relative probability of observing processes that have positive (A) and negative (− A) total dissipation in non-equilibrium systems [2,3]:. The integral in (3) involves an instantaneous dissipation function:. It follows that the Second Law is correct as either an ensemble, or a temporal, or a volume average.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
