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<p>We introduce a “two-particle factorization” condition which allows us to formulate the homogeneous Boltzmann equation for non-reversible collision kernels in terms of an entropy inequality. This formulation yields an H-Theorem. We provide some examples of non-reversible binary collision models with a concentration/dispersion mechanism, as in opinion dynamics, which satisfy this condition. As a preliminary step, we also provide an analogous variational formulation of non-reversible continuous time Markov chains, expressed in terms of an entropy dissipation inequality.</p>

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Entropy Dissipation Inequality for General Binary Collision Models

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年8月4日

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  • Giada Basile,
  • Dario Benedetto

摘要

We introduce a “two-particle factorization” condition which allows us to formulate the homogeneous Boltzmann equation for non-reversible collision kernels in terms of an entropy inequality. This formulation yields an H-Theorem. We provide some examples of non-reversible binary collision models with a concentration/dispersion mechanism, as in opinion dynamics, which satisfy this condition. As a preliminary step, we also provide an analogous variational formulation of non-reversible continuous time Markov chains, expressed in terms of an entropy dissipation inequality.