Nernst heat theorem for small non-equilibrium systems

Abstract:
The Nernst formulation of Third Law states that as the ambient temperature approaches absolute zero, thermodynamic processes become increasingly reluctant to exchange heat with the environment. Entropy and various response functions, such as heat capacity, progressively vanish in this regime. In my talk, I will discuss how to extend these basic concepts to thermodynamic transformations between steady states of small non-equilibrium systems weakly coupled to a heat reservoir. Using a standard stochastic-thermodynamic framework, we define the reversible component of heat transfer in the quasistatic limit, and we show that it is both "geometric" and, in principle, operationally accessible through frequency dependent calorimetry [1]. We will demonstrate the theory on simple models of driven and active particles [2] and formulate conditions for which the reversible heat and associated non-equilibrium heat capacity vanish in the zero-temperature limit [3]. In simple terms, it requires that the heat dissipated along typical relaxation paths cannot dramatically differ between different initial states.

[1] C. Maes and K. Netočný, J. Stat. Mech., 2019, 114004 (2019).
[2] P. Dolai, C. Maes, and K. Netočný, arXiv:2208.01583, to appear in SciPost Phys.
[3] F. Khodabandehlou, C. Maes, and K. Netočný, arXiv:2207.10313, to appear in J. Chem. Phys.