Anomalous transport phenomenon of a charged Brownian particle under a thermal gradient and a magnetic field

[1] U. Seifert, Stochastic thermodynamics, fluctuation theorems, and molecular machines, Rep. Prog. Phys. 75, 126001 (2012).

[2] K. Sekimoto, Stochastic Energetics, Lecture Notes in Physics, Vol. 799 (Springer, Berlin, 2010).

[3] R. Klages, W. Just, and C. Jarzynski, Nonequilibrium Statistical Physics of Small Systems (Wiley, New York, 2013).

[4] V. Y. Chernyak, M. Chertkov, and C. Jarzynski, Path-integral analysis of fluctuation theorems for general Langevin processes, J. Stat. Mech.: Theory Exp. (2006) P08001.

[5] H. M. Chun, X. Durang, and J. D. Noh, Emergence of nonwhite noise in Langevin dynamics with magnetic Lorentz force, Phys. Rev. E 97, 032117 (2018).

[6] S. Tamaki and K. Saito, Nernst-like effect in a flexible chain, Phys. Rev. E 98, 052134 (2018).

[7] A. Souslov, K. Dasbiswas, M. Fruchart, S. Vaikuntanathan, and V. Vitelli, Topological Waves in Fluids with Odd Viscosity, Phys. Rev. Lett. 122, 128001 (2019).

[8] I. Abdoli, H. D. Vuijk, J. U. Sommer, J. M. Brader, and A. Sharma, Nondiffusive fluxes in a Brownian system with Lorentz force, Phys. Rev. E 101, 012120 (2020).

[9] H. D. Vuijk, J. U. Sommer, H. Merlitz, J. M. Brader, and A. Sharma, Lorentz forces induce inhomogeneity and flux in active systems, Phys. Rev. Research 2, 013320 (2020).

[10] P. Pradhan and U. Seifert, Nonexistence of classical diamag- netism and nonequilibrium fluctuation theorems for charged particles on a curved surface, EPL 89, 37001 (2010).

[11] L. Onsager, Reciprocal relations in irreversible processes. I, Phys. Rev. 37, 405 (1931).

[12] L. Onsager, Reciprocal relations in irreversible processes. II, Phys. Rev. 38, 2265 (1931).

[13] N. van Kampen, Relative stability in nonuniform temperature, IBM J. Res. Dev. 32, 107 (1988).

[14] N. G. van Kampen, Explicit calculation of a model for dif- fusion in nonconstant temperature, J. Math. Phys. 29, 1220 (1988).

[15] K. Miyazaki, Y. Nakayama, and H. Matsuyama, Entropy anomaly and linear irreversible thermodynamics, Phys. Rev. E 98, 022101 (2018).

[16] S. R. de Groot and P. Mazur, Nonequilibrium Thermodynamics (Dover, New York, 1962).

[17] L. Pitaevskii and E. Lifshitz, Physical Kinetics, Course of Theoretical Physics, Vol. 10 (Elsevier Science, Amsterdam, 2012).

[18] K. Behnia and H. Aubin, Nernst effect in metals and super- conductors: A review of concepts and experiments, Rep. Prog. Phys. 79, 046502 (2016).

[19] R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics, 2nd ed., Solid State Sci- ences (Springer Science & Business Media, Berlin, 1991), Vol. 30.

[20] J. Hansen and I. McDonald, Theory of Simple Liquids: With Ap- plications to Soft Matter (Elsevier Science, Amsterdam, 2013).

[21] H. Risken, The Fokker-Planck Equation: Methods of Solutions and Applications, 2nd ed. (Springer, Berlin, 1996).

[22] H. Brinkman, Brownian motion in a field of force and the diffusion theory of chemical reactions, Physica 22, 29 (1956).

[23] X. Durang, C. Kwon, and H. Park, Overdamped limit and inverse-friction expansion for Brownian motion in an inhomo- geneous medium, Phys. Rev. E 91, 062118 (2015).

[24] K. Kaneko, Adiabatic elimination by the eigenfunction expan- sion method, Prog. Theor. Phys. 66, 129 (1981).

[25] M. E. Widder and U. M. Titulaer, Brownian motion in a medium with inhomogeneous temperature, Phys. A (Amsterdam, Neth.) 154, 452 (1989).

[26] G. Stolovitzky, Non-isothermal inertial Brownian motion, Phys. Lett. A 241, 240 (1998).

[27] S. van Teeffelen and H. Löwen, Dynamics of a Brownian circle swimmer, Phys. Rev.E 78, 020101(R) (2008).

[28] H. Löwen, Chirality in microswimmer motion: From circle swimmers to active turbulence, Eur. Phys. J. Spec. Top. 225, 2319 (2016).

[29] Q. Yang, H. Zhu, P. Liu, R. Liu, Q. Shi, K. Chen, N. Zheng, F. Ye, and M. Yang, Topologically Protected Transport of Cargo in a Chiral Active Fluid Aided by Odd-Viscosity-Enhanced Depletion Interactions, Phys. Rev. Lett. 126, 198001 (2021).

[30] M. Huang, W. Hu, S. Yang, Q.-X. Liu, and H. P. Zhang, Circular swimming motility and disordered hyperuniform state in an algae system, Proc. Natl. Acad. Sci. USA 118, e2100493118 (2021).

[31] S. Mandal, B. Liebchen, and H. Löwen, Motility-Induced Tem- perature Difference in Coexisting Phases, Phys. Rev. Lett. 123, 228001 (2019).

[32] H. Löwen, Inertial effects of self-propelled particles: From ac- tive Brownian to active Langevin motion, J. Chem. Phys. 152, 040901 (2020).