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Geometric Decomposition of Nonlinearity in Thermodynamic Average w.r.t. Entanglement in Structural Degree of Freedoms

Abstract: While nonlinearity in thermodynamic average generally decrease with decreasing
        non-separability in s.d.f, contribution from the non-separability to nonlinearity has not been clarified at all.
        We show that by employing dual flat statistical manifold, nonlinearity can be decomposed into sum of
        contribution from canonical non-separability in s.d.f. and that from deviation in gaussian canonical distribution.
[K. Yuge, arXiv:1811.09612 [cond-mat.stat-mech]. ]








Discrete Thermodynamic System Revisited from Tropical Geometry

Abstract: Nonlinearity in thermodynamic average plays central role for macroscopic properties,
        while it is still unclear how its entire behavior is dominated by geometry of underlying lattice.
        We derive that by applying suitable limit in tropical geometry to vector field D,
        conecction between nonlinearity and lattice geometry is elucidated.
[K. Yuge and S. Ohta, J. Phys. Soc. Jpn. 89, 084802 (2020). ]








Bidirectional-stability Breaking in Thermodynamic Average

Motivation: For classical many-body systems, how thermodynamic average connects a set of potential energy surface
        and a set of structure in thermodynamic equilibrium? Can we formulate the connection without any thermodynamic
        information (i.e., formulate connection from configurational geometry)?
Answer: Yes. The connection can be formulated through new vector field constructed only from configurational geometry.

[K. Yuge, J. Phys. Soc. Jpn. 87, 104802 (2018). ]
[K. Yuge and S. Ohta, J. Phys. Soc. Jpn. 88, 104803 (2019). ]









Graph Representaion for Configurational Properties

[K. Yuge, J. Phys. Soc. Jpn. 86, 024802 (2017). ]






Projection State

Motivation: To break the curse of dimensionality in classical statistical thermodynamics, can we a priori know
        a special microscopic state to characterize physical quantity in equilibrium states?
[K. Yuge, J. Phys. Soc. Jpn. 85, 024802 (2016). ]
[T. Taikei, T. Kishimoto, K. Takeuchi and K. Yuge, J. Phys. Soc. Jpn. 86, 114802 (2017). ]



Matrix Representation of Canonical Average for discrete systems

Motivation: Can we obtain explicit matrix form of thermodynamic (canonical) average for discrete system at given T?
[K. Yuge, J. Phys. Soc. Jpn. 85, 024802 (2016). ]
[K. Yuge, arXiv:1611.08362 [cond-mat.dis-nn] ]



Structure Integration

Direct determination of partition function Z by decomposing structural degree of freedom.
[K. Takeuchi, R. Tanaka and K. Yuge, J. Phys.: Condens. Matter 27, 385201 (2015).]
[K. Yuge, J. Phys. Soc. Jpn. 84, 084801 (2015). ]



Variable-lattice Generalized Ising Model (VLGIM)

Motivation: GIM Hamiltonian depends on lattice: Linkage for physical quantity on multiple lattices is unclear.
[K. Yuge, Phys. Rev. B 85, 144105 (2012). ]
[K. Yuge et al., Phys. Rev. B 87, 024105 (2013). ]



Joint free energy gain

Motivation: How to universally characterize solubility for coexistence of strong and weak ordering in multicomponent system?
[K. Yuge, Phys. Rev. B 84, 134207 (2011).]




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