33 citations · 199 across the 35 of their papers we have counts for
35 papers
Contact geometric approach to Glauber dynamics near a cusp and its limitation
Shin-itiro Goto, Shai Lerer, Leonid Polterovich
We study a nonequilibrium mean field Ising model in the low temperature phase regime, where metastable equilibrium states develop a cuspidal (spinodal) singularity. We focus on cel…
Affine geometric description of thermodynamics
Shin-itiro Goto
Thermodynamics provides a unified perspective of thermodynamic properties of various substances. To formulate thermodynamics in the language of sophisticated mathematics, thermodyn…
Nonequilibrium thermodynamic process with hysteresis and metastable states -- A contact Hamiltonian with unstable and stable segments of a Legendre submanifold
Shin-itiro Goto
In this paper, a dynamical process in a statistical thermodynamic system of spins exhibiting a phase transition is described on a contact manifold, where such a dynamical process i…
Fast symplectic integrator for Nesterov-type acceleration method
Shin-itiro Goto, Hideitsu Hino
In this paper, explicit stable integrators based on symplectic and contact geometries are proposed for a non-autonomous ordinarily differential equation (ODE) found in improving co…
Diffusion equations from master equations -- A discrete geometric approach --
Shin-itiro Goto, Hideitsu Hino
In this paper, continuous-time master equations with finite states employed in nonequilibrium statistical mechanics are formulated in the language of discrete geometry. In this for…
Expectation variables on a para-contact metric manifold exactly derived from master equations
Shin-itiro Goto, Hideitsu Hino
Based on information and para-contact metric geometries, in this paper a class of dynamical systems is formulated for describing time-development of expectation variables. Here suc…