The Onsager's reciprocal relation plays a fundamental role in the nonequilibrium thermodynamics. However, unfortunately, its classical version is valid only within a narrow region near equilibrium due to the linear regression hypothesis, which largely restricts its usage. In this paper, based on the conservation-dissipation formalism, a generalized version of Onsager's relations for the master equations and Fokker-Planck equations was derived. Nonlinear constitutive relations with nonsymmetric and positively stable operators, which become symmetric under the detailed balance condition, constitute key features of this new generalization. Similar conclusions also hold for many other classical models in physics and chemistry, which in turn make the current study as a benchmark for the application of generalized Onsager's relations in nonequilibrium thermodynamics.

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Often times, the ability to distinguish between random data and a public key can leads to an attack against the cryptosystem itself. In this paper, we will show experimentally a very efficient distinguisher based on the distribution of ranks of the symmetric matrices associated with the central map in the multivariate cryptosystem HFE when the degree D of the central map is very small.

Given a smooth projective variety X and a smooth divisor D\subset X. We study relative Gromov-Witten invariants of (X,D) and the corresponding orbifold Gromov-Witten invariants of the r-th root stack X_{D,r}. For sufficiently large r, we prove that orbifold Gromov- Witten invariants of X_{D,r} are polynomials in r. Moreover, higher genus relative Gromov-Witten invariants of (X,D) are exactly the constant terms of the corresponding higher genus orbifold Gromov-Witten invari- ants of X_{D,r}. We also provide a new proof for the equality between genus zero relative and orbifold Gromov-Witten invariants, originally proved by Abramovich-Cadman-Wise. When r is sufficiently large and X=C is a curve, we prove that stationary relative invariants of C are equal to the stationary orbifold invariants in all genera.