Symmetry classes of classical stochastic processes

Sá, Lucas (avtor), Ribeiro, Pedro (avtor), Prosen, Tomaž (avtor), Bernard, Denis (avtor)

We perform a systematic symmetry classification of the Markov generators of classical stochastic processes. Our classification scheme is based on the action of involutive symmetry transformations of a real Markov generator, extending the Bernard-LeClair scheme to the arena of classical stochastic processes and leading to a set of up to fifteen allowed symmetry classes. We construct families of solutions of arbitrary matrix dimensions for five of these classes with a simple physical interpretation of particles hopping on multipartite graphs. In the remaining classes, such a simple construction is prevented by the positivity of entries of the generator particular to classical stochastic processes, which imposes a further requirement beyond the usual symmetry classification constraints. We partially overcome this difficulty by resorting to a stochastic optimization algorithm, finding specific examples of generators of small matrix dimensions in six further classes, leaving the existence of the final four allowed classes an open problem. Our symmetry-based results unveil new possibilities in the dynamics of classical stochastic processes: Kramers degeneracy of eigenvalue pairs, dihedral symmetry of the spectra of Markov generators, and time reversal properties of stochastic trajectories and correlation functions.

• Jezik: Angleški jezik
• Ključne besede: statistical physics, stochastic processes
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2025
• Št. strani: 26 str.
• Številčenje: Vol. 192, art. no. 41
• PID: 20.500.12556/RUL-175282
• UDK: 536
• ISSN pri članku: 1572-9613
• DOI: 10.1007/s10955-025-03423-y
• COBISS.SI-ID: 254405635
• Datum objave v RUL: 23.10.2025

Gradivo je del revije

• Naslov: Journal of statistical physics : Elektronski vir
• Skrajšan naslov: J. stat. phys.
• Založnik: Kluwer
• ISSN: 1572-9613
• COBISS.SI-ID: 513205529

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: statistična fizika, stohastični procesi