{"ID":23523534,"CreatedAt":"2026-09-18T02:58:45.531918055Z","UpdatedAt":"2026-09-18T02:58:45.531918055Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20681","arxiv_id":"2609.20681","title":"Martingale theory for heat and phase-space contraction in heterogeneous diffusions","abstract":"We investigate martingale properties of heat dissipated by generic non-equilibrium overdamped Langevin dynamics with multiple dimensions and transport coefficients that may depend explicitly on time and/or space. We find quantitative criteria that establish that heat dissipation may exhibit transient martingale (time-conserved), submartingale (time increasing), and supermartingale (time decreasing) properties in Langevin dynamics with drift coefficients with spatial non-linear dependencies. Furthermore, we reveal a tight link between the heat statistics at stopping (e.g. first-passage) times with that of a functional quantifying the phase-space contraction in the system dynamics. The theoretical results are used to predict the statistical properties of the heat dissipated by a spherical microscopic particle subject to gravity and double-layer forces and hydrodynamically interacting with a rigid wall, whose validity is confirmed by numerical simulations. These results extend the scope of stochastic energetics by revealing a non-trivial relation between heat fluctuations' statistical properties and the non-linear features of non-equilibrium processes.","short_abstract":"We investigate martingale properties of heat dissipated by generic non-equilibrium overdamped Langevin dynamics with multiple dimensions and transport coefficients that may depend explicitly on time and/or space. We find quantitative criteria that establish that heat dissipation may exhibit transient martingale (time-c...","url_abs":"https://arxiv.org/abs/2609.20681","url_pdf":"https://arxiv.org/pdf/2609.20681v1","authors":"[\"Jing Qin\",\"Nariya Uchida\",\"Édgar Roldán\"]","published":"2026-09-17T16:51:33Z","proceeding":"cond-mat.stat-mech","tasks":"[\"cond-mat.stat-mech\"]","methods":"[\"Diffusion Model\"]","has_code":false}