Abstract
We define thermodynamic configurations and identify two primitives of discrete quantum processes between configurations for which heat and work can be defined in a natural way. This allows us to uncover a general second law for any discrete trajectory that consists of a sequence of these primitives, linking both equilibrium and non-equilibrium configurations. Moreover, in the limit of a discrete trajectory that passes through an infinite number of configurations, i.e. in the reversible limit, we recover the saturation of the second law. Finally, we show that for a discrete Carnot cycle operating between four configurations one recovers Carnot's thermal efficiency.
Highlights
The intuitive meaning of heat and work in thermodynamics is that of two types of energetic resources, one fully controllable and useful, the other uncontrolled and wasteful
First we show that entropic inequalities when applied to discrete trajectories formed by concatenating Discrete Unitary Transformations (DUTs) and Discrete Thermalising Transformations (DTTs) yields the second law of thermodynamics in the Clausius formulation
Having identified two fundamental process primitives in configuration space, we focus on more complex discrete trajectories. These can start from equilibrium or non-equilibrium configurations, we restrict ourselves to discrete trajectories that can be obtained by concatenating DUT and DTTs
Summary
The intuitive meaning of heat and work in thermodynamics is that of two types of energetic resources, one fully controllable and useful, the other uncontrolled and wasteful. An impressive effort has been devoted to provide a consistent mathematical characterisation of these notions within a quantum mechanical description of physics [1,2,3,4,5,6,7] This is a challenge since in contrast to other thermodynamic quantities, such as internal energy and entropy, heat and work are not properties of individual states of a system. (We will neglect here the possibility of monitoring through continuous weak measurements.) For discrete snapshots of the dynamics, we find that by decomposing the transition into possible sequences of two fundamental primitives, it is possible to define heat and work for the discrete process in a way that is experimentally and mathematically clear This allows us to establish a general second law for discrete processes between equilibrium and non-equilibrium states and the analysis of a.
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