Quantum confinement and negative heat capacity

Abstract

Thermodynamics dictates that the specific heat of a system is strictly non-negative. However, in finite classical systems there are well known theoretical and experimental cases where this rule is violated, in particular finite atomic clusters. Here, we show for the first time that negative heat capacity can also occur in finite quantum systems. The physical scenario on which this effect might be experimentally observed is discussed. Observing such an effect might lead to the design of new light harvesting nano devices, in particular a solar nano refrigerator.Thermodynamics dictates that the specific heat of a system is strictly non-negative, implying that the addition (subtraction) of energy cannot result in a decrease (increase) of the system's temperature [1]. Nevertheless there are well known cases where this rule is apparently violated [2,3]. For example, this phenomenom occurs at the nanoscale and it was eloquently showed by Schmidt et al. who, in an elegant series of experiments, determined a negative heat capacity of a Na cluster with 147 atoms for temperatures neighboring the melting temperature of the cluster [4][5][6]. Also at the astronomical scale negative heat capacities have been known for years [7], where it is observed that stars and star clusters increase their temperature as they age while loosing energy by radiation [8]. Therefore, invoking the thermodynamic limit is not sufficient to guarantee the equivalence of Canonical and Microcanonical ensembles. The key to theoretically reconcile these results with the thermodynamics was addressed by Thirring and coworkers: A system may display negative heat capacity, even in the thermodynamics limit, provided that it is not ergodic [9][10][11]. The ambiguity of negative heat capacity concept has been extensively examined by the work of RS Berry and coworkers [24][25][26][27][28][29] . In this letter we investigate whether this phenomenon could also be observed in the quantum domain, in particular, for small systems. An important motivation for the understanding and control of this phenomenon would be the implementation of refrigeration strategies at the nano scale, for example for light harvesting nano devices that would benefit from an inverted thermal response.Following previous ideas [12, 13] on a minimal model having negative specific heat for classical systems we study the effect of the delocalization of the wave function on the average kinetic energy of the system, and also on several definitions of temperature corresponding to the Canonical and Microcanonical statistics. Let us consider a 1d potential well trapped between impenetrable walls:This potential represents a simple example that suffices to show how a negative heat capacity emerges. The solution of the Schrödinger equation for one particle in V (x) given by Eq. (1) can be * kais@purdue.edu

Anomalous vacuum energy and stability of a quantum liquid

“…Interestingly, negative specific heat has been found to operate in small or out-of-equilibrium systems [10][11][12][13][14].…”

“…Second, previous discussions have attributed negative heat capacity to the non-equilibrium state of the system or its smallness in terms of the number of atoms [10][11][12][13][14].…”

Entropy behavior for isolated systems containing bounded and unbounded states: latent heat at the inflection point

“…It should be noted that the existence of negative specific heat [2,25,26] has been considered, for example, in clusters of sodium atoms near the liquid-solid transition [3] and clusters of Ar 39 [4]. More examples include finite systems [5], hydrophilic interactions [27], small isolated systems [6,28] and left-handed structures [29,30]. However, there is theoretical evidence that in the case of nanoclusters the specific negative heat is the abrupt result of changes in the phase space volume [31].…”

“…However, there is theoretical evidence that in the case of nanoclusters the specific negative heat is the abrupt result of changes in the phase space volume [31]. In this is line, Schmidt et al, in an well-dressed series of experiments, determined a negative heat capacity of a Na cluster with 147 atoms for temperatures near the melting temperature of the cluster [6]. Stability and fluctuation-dissipation have been similarly considered [32,33] and, additionally, discussed under the canonical ensemble framework [34].…”

“…Many physical systems show a change in the concavity of the entropy as a function of the energy with important thermodynamic implications (star, isolated clusters, cluster of 147 sodium atoms, Ar39 cluster, small systems, finite quantum systems, magnetically self-confined plasma [1][2][3][4][5][6][7]). The concavity's point of change-the inflection point-becomes directly related to the divergence of the specific heat.…”