Constructor Theory of Thermodynamics

TL;DR

This paper introduces a new, scale-independent formulation of thermodynamics based on constructor theory, providing precise definitions of work, heat, and a link between information theory and the first law, improving foundational understanding.

Contribution

It offers a non-approximative, scale-independent axiomatic framework for thermodynamics using constructor theory, unifying existing approaches and clarifying fundamental concepts.

Findings

Provides a non-approximative definition of adiabatic accessibility

Establishes a clear distinction between work and heat without scale assumptions

Reveals a connection between information theory and the first law of thermodynamics

Abstract

All current formulations of thermodynamics invoke some form of coarse-graining or ensembles as the supposed link between their own laws and the microscopic laws of motion. They deal only with ensemble-averages, expectation values, macroscopic limits, infinite heat baths, etc., not with the details of physical variables of individual microscopic systems. They are consistent with the laws of motion for finite systems only in certain approximations, which improve with increasing scale, given various assumptions about initial conditions which are neither specified precisely nor even thought to hold exactly in nature. Here I propose a new formulation of the zeroth, first and second laws, improving upon the axiomatic approach to thermodynamics (Carath\'eodory, 1909; Lieb & Yngvason, 1999), via the principles of the recently proposed constructor theory. Specifically, I provide a non-approximative, scale-independent formulation of 'adiabatic accessibility'; this in turn provides a non-approximative, scale-independent distinction between work and heat and reveals an unexpected connection between information theory and the first law of thermodynamics (not just the second). It also achieves the long-sought unification of the axiomatic approach with Kelvin's.