Two approaches to quantum Generalization of thermodynamics

Koji Maruyama, Časlav Brukner, Vlatko Vedral

Thermodynamics is a macroscopic physical theory whose two very general laws are independent of any underlying dynamical laws and structures. Nevertheless, its generality enables us to understand a broad spectrum of phenomena in physics, information science and biology. Does thermodynamics then imply any results in quantum information theory? Taking accessible information in a system as an example, we show that thermodynamics implies a weaker bound on it than the quantum mechanical one (the Holevo bound). In other words, if any post-quantum physics should allow more information storage it could still be under the umbrella of thermodynamics.

A. D. Jannussis

A. Gamba

Mohammad Mehboudi, Harry J. D. Miller

Constructing optimal thermodynamic processes in quantum systems relies on managing the balance between the average excess work and its stochastic fluctuations. Recently it has been shown that two different quantum generalizations of thermodynamic length can be utilized to determine protocols with either minimal excess work or minimal work variance. These lengths measure the distance between points on a manifold of control parameters, and optimal protocols are achieved by following the relevant geodesic paths given some fixed boundary conditions. Here we explore this problem in the context of Gaussian quantum states that are weakly coupled to an environment and derive general expressions for these two forms of thermodynamic length. We then use this to compute optimal thermodynamic protocols for various examples of externally driven Gaussian systems with multiple control parameters.

I. Tkachenko, Yu. Miroshnichenko, Boris Drenchev +2 more

Based on the fundamental physical notions and the early developed general approach for analyzing a transient development in an open thermodynamic system, equivalence of the two formulations of the uncertainty principle in general physics was shown.Necessity of time quantum introduction proceeding from the uncertainty principle combined with the approach was grounded and an analytical formula to evaluate its numerical value was derived from the relation connecting uncertainties of energy and time.Using the approach, two ways for the obtained formula justification were proposed and numerically verified.Mandatory existence of the time quantum at beginning stages of the thermodynamic system evolution and its disappearing at the finishing ones was noted.Reciprocal dependence of the time quantum value on the energy of an open thermodynamic system is also emphasized that is in accordance with general physical notions.Coincidence was shown of the numerical data for some fundamental characteristics evaluated using the derived relations with * Corresponding author.

Peter Hertel