Laws of thermodynamics for exponential families

• URL: http://arxiv.org/abs/2501.02071v1
• Date: Fri, 03 Jan 2025 19:36:09 GMT
• Title: Laws of thermodynamics for exponential families
• Authors: Akshay Balsubramani,
• Abstract summary: We develop the laws of thermodynamics in terms of general exponential families.<n>We extend the well-known way in which exponential families characterize thermodynamic and learning equilibria.<n>These ideas have broad implications for quantifying and addressing distribution shift.
• Score: 2.092840468195572
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop the laws of thermodynamics in terms of general exponential families. By casting learning (log-loss minimization) problems in max-entropy and statistical mechanics terms, we translate thermodynamics results to learning scenarios. We extend the well-known way in which exponential families characterize thermodynamic and learning equilibria. Basic ideas of work and heat, and advanced concepts of thermodynamic cycles and equipartition of energy, find exact and useful counterparts in AI / statistics terms. These ideas have broad implications for quantifying and addressing distribution shift.

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