{"paper":{"title":"Thermodynamics and Geometry of Reversible and Irreversible Markov Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hao Ge, Hong Qian, Woo H. Kim","submitted_at":"2011-08-19T21:48:45Z","abstract_excerpt":"Master equation with microscopic reversibility ($q_{ij}\\neq 0$ iff $q_{ji}\\neq 0$) has a {\\em thermodynamic superstructure} in terms of two state functions $S$, entropy, and $F$, free energy: It is discovered recently that entropy production rate $e_p=-dF/dt+Q_{hk}$ with both $-dF/dt=f_d, Q_{hk} \\ge 0$. The free energy dissipation $f_d\\ge 0$ reflects irreversibility in spontaneous self-organization; house-keeping heat $Q_{hk}\\ge 0$ reveals broken time-symmetry in open system driven away from equilibrium. In a Riemannian geometric space, the master equation is a geodesic flow when $Q_{hk}=0$; h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4055","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}